lOMoARcPSD|26927854 ALL TEST BANK Decision - final exam Decesion MAking (دوعس كلملا ةعماج) Scan to open on Studocu Studocu is not sponsored or endorsed by any college or university Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Introduction to Management Science, 13e, Global Edition (Taylor) Chapter 1 Management Science 1) A management science solution can be either a recommended decision or information that helps a manager make a decision. Answer: TRUE Diff: 2 Page Ref: 25 Section Heading: The Management Science Approach to Problem Solving Keywords: model, management science techniques AACSB: Analytical thinking 2) A variable is a value that is usually a coefficient of a parameter in an equation. Answer: FALSE Diff: 1 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: variable AACSB: Analytical thinking 3) Parameters are known, constant values that are usually coefficients of variables in equations. Answer: TRUE Diff: 1 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: parameter AACSB: Analytical thinking 4) Data are pieces of information from the problem environment. Answer: TRUE Diff: 1 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: data AACSB: Analytical thinking 5) A model is a mathematical representation of a problem situation including variables, parameters, and equations. Answer: TRUE Diff: 1 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: model, management science techniques AACSB: Analytical thinking 6) A management science technique usually applies to a specific model type. Answer: TRUE Diff: 1 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: models, management science techniques AACSB: Analytical thinking 1 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 7) The first step of the management science process is to define the problem. Answer: FALSE Diff: 2 Page Ref: 22 Section Heading: The Management Science Approach to Problem Solving Keywords: management science process AACSB: Analytical thinking 8) The term big data refers to numbers of large magnitude, i.e., greater than or equal to one billion. Answer: FALSE Diff: 1 Page Ref: 27 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge 9) A key component of business analytics is the recent availability of large amounts of data. Answer: TRUE Diff: 1 Page Ref: 27 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge 10) Business analytics brings together the disciplines of information systems, management science, statistics, and mathematical modeling. Answer: TRUE Diff: 1 Page Ref: 27 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge 11) Management science modeling techniques provide results that are known with certainty. Answer: FALSE Diff: 2 Page Ref: 38 Section Heading: Management Science Modeling Techniques Keywords: management science modeling techniques, certainty AACSB: Analytical thinking 12) The term sensitivity analysis refers to testing how a problem solution reacts to changes in one or more of the model parameters. Answer: TRUE Diff: 1 Page Ref: 32 Section Heading: Model Building: Break-Even Analysis Keywords: sensitivity analysis, parameter changes AACSB: Application of knowledge 2 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 13) Variable costs depend on the number of items produced. Answer: TRUE Diff: 1 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: variable cost, break-even analysis AACSB: Application of knowledge 14) Fixed cost is the difference between total cost and total variable cost. Answer: TRUE Diff: 1 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: total cost, break-even analysis AACSB: Application of knowledge 15) The break-even point is the volume that equates total revenue with total cost. Answer: TRUE Diff: 1 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 16) In general, an increase in price increases the break-even point if all costs are held constant. Answer: FALSE Diff: 1 Page Ref: 32 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 17) If variable costs increase, but price and fixed costs are held constant, the break-even point will decrease. Answer: FALSE Diff: 2 Page Ref: 32 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 18) Managers utilize spreadsheets to conduct their own analyses in management science studies. Answer: TRUE Diff: 2 Page Ref: 34 Section Heading: Computer Solution Keywords: spreadsheets AACSB: Analytical thinking 3 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 19) Management science techniques focus primarily on observation, model construction, and implementation to find an appropriate solution to a problem. Answer: FALSE Diff: 2 Page Ref: 36 Section Heading: Management Science Modeling Techniques Keywords: management science modeling techniques, steps of the scientific method AACSB: Analytical thinking 20) Management science modeling techniques focus on model construction and problem solution. Answer: TRUE Diff: 2 Page Ref: 36 Section Heading: Management Science Modeling Techniques Keywords: management science model techniques, model construction, problem solution AACSB: Analytical thinking 21) A typical objective function might be written as 3S + 2R + 5Z ≤ 20. Answer: FALSE Diff: 2 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: objective function AACSB: Analytical thinking 22) Decision Support Systems (DSS) use computers to help decision makers address complex problems. Answer: TRUE Diff: 1 Page Ref: 41 Section Heading: Management Science Models in Decision Support Systems Keywords: decision making, management science AACSB: Application of knowledge 23) In both an objective function and a constraint, the decision variables are represented by numbers. Answer: FALSE Diff: 1 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: decision variables AACSB: Analytical thinking 24) A DSS is a type of ERP system. Answer: FALSE Diff: 2 Page Ref: 42 Section Heading: The Management Science Approach to Problem Solving Keywords: DSS, ERP AACSB: Analytical thinking 4 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 25) A key element of a decision support system (DSS) is the person using the system. Answer: TRUE Diff: 2 Page Ref: 41 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking 26) An ERP system is software that is capable of connecting functions and processes across an entire company. Answer: TRUE Diff: 1 Page Ref: 42 Section Heading: The Management Science Approach to Problem Solving Keywords: ERP, enterprise resource planning AACSB: Analytical thinking 27) A company may use an intranet for communication among its own business units that are scattered geographically. Answer: TRUE Diff: 1 Page Ref: 42 Section Heading: The Management Science Approach to Problem Solving Keywords: intranet AACSB: Analytical thinking 28) ________ are pieces of information from the problem environment. Answer: Data Diff: 1 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: data AACSB: Application of knowledge 29) A(n) ________ is a functional relationship including variables, parameters, and equations. Answer: model Diff: 1 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: model AACSB: Application of knowledge 30) ________ is the term used to describe a collection of numbers that is massive in size. Answer: Big data Diff: 1 Page Ref: 27 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge 5 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 31) ________ uses large amounts of data with management science techniques and modeling to help managers make decisions. Answer: Business analytics Diff: 1 Page Ref: 27 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge 32) Management science techniques include ________ techniques, models that are represented as diagrams, presenting a pictorial representation of the system being analyzed. Answer: network Diff: 1 Page Ref: 36 Section Heading: Management Science Modeling Techniques Keywords: management science, networks AACSB: Application of knowledge 33) An increase in output typically results in an increase in the ________ cost. Answer: total variable, total Diff: 1 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 34) ________ techniques provide results that contain uncertainty, unlike mathematical programming techniques which are deterministic. Answer: Probabilistic Diff: 1 Page Ref: 38 Section Heading: Management Science Modeling Techniques Keywords: management science techniques, probabilistic techniques AACSB: Analytical thinking 35) ________ costs are independent of the volume of goods produced and remain constant. Answer: Fixed Diff: 1 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: fixed cost, break-even analysis AACSB: Analytical thinking 36) Total revenue minus total cost equals ________. Answer: profit Diff: 1 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: profit, break-even analysis AACSB: Analytical thinking 6 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 37) The ________ is the volume that equates total revenue with total cost. Answer: break-even point Diff: 1 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 38) A(n) ________ represents a limitation to achieving maximum profits due to limited resources. Answer: constraint Diff: 1 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: constraint, model development AACSB: Analytical thinking 39) One way to test how a management science model reacts to changes in its parameters is to conduct ________ analysis. Answer: sensitivity Diff: 1 Page Ref: 32 Section Heading: Model Building: Break-Even Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 40) ________ consist of models that are represented as diagrams rather than as strictly mathematical techniques. Answer: Networks Diff: 2 Page Ref: 36 Section Heading: Management Science Modeling Techniques Keywords: network flow models AACSB: Analytical thinking 41) A management science technique that does not assume that all parameters are known with certainty is a(n) ________ technique. Answer: probabilistic Diff: 2 Page Ref: 38 Section Heading: Management Science Modeling Techniques Keywords: probabilistic techniques AACSB: Analytical thinking 42) A(n) ________ is a computer-based system that helps decision-makers address complex problems that involve different parts of an organization and operations. Answer: decision support system, DSS Diff: 1 Page Ref: 41 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking 7 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 43) The databases, management science models, and internet interact with the decision maker via the ________. Answer: user interface Diff: 2 Page Ref: 42 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support system, user interface AACSB: Analytical thinking 44) ________ systems connect the business functions of an entire company. Answer: Enterprise resource planning, ERP Diff: 1 Page Ref: 41 Section Heading: Management Science Models in Decision Support Systems Keywords: ERP, enterprise resource planning AACSB: Analytical thinking 45) The steps of the management science process are: A) problem definition, model construction, observation, model solution, implementation. B) observation, problem definition, model construction, model solution, implementation. C) model construction, problem definition, observation, model solution, implementation. D) observation, implementation, problem definition, model construction, model solution. Answer: B Diff: 1 Page Ref: 22 Section Heading: The Management Science Approach to Problem Solving Keywords: steps of sci method, problem solving approach, management sci process AACSB: Analytical thinking 46) A model is a functional relationship that includes: A) variables. B) parameters. C) equations. D) all of the above Answer: D Diff: 1 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: model AACSB: Analytical thinking 8 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 47) Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model? A) a decision variable B) an objective function C) a constraint D) a parameter Answer: C Diff: 2 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: model, constraint AACSB: Analytical thinking 48) There is considerable overlap in the scientific method and management science techniques. Which of the following steps is shared between them? A) observation B) problem definition C) model construction D) implementation Answer: C Diff: 2 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: scientific approach AACSB: Analytical thinking 49) Which of the following is incorrect with respect to the use of models in decision making? A) They improve understanding of the problem. B) They promote subjectivity in decision making. C) They are generally easy to use. D) They provide a systematic approach to problem solving. Answer: B Diff: 3 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: model, problem solving AACSB: Analytical thinking 50) The field of management science: A) approaches decision making irrationally with techniques based on the scientific method. B) is another name for management or human resources management. C) concentrates on the use of quantitative methods to assist managers in decision making. D) is completely separate and distinct from all other disciplines. Answer: C Diff: 1 Page Ref: 22 Section Heading: The Management Science Approach to Problem Solving Keywords: management science, operations research AACSB: Analytical thinking 9 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 51) The processes of problem observation: A) cannot be done until alternatives are proposed. B) requires consideration of multiple criteria. C) is the first step of decision making. D) is the final step of problem solving. Answer: C Diff: 1 Page Ref: 22 Section Heading: The Management Science Approach to Problem Solving Keywords: observation, problem observation, management science process AACSB: Analytical thinking 52) The limits of the problem and the degree to which it pervades other units in the organization must be included during the ________ step of the management science process. A) observation B) definition C) solution D) implementation Answer: B Diff: 1 Page Ref: 22 Section Heading: The Management Science Approach to Problem Solving Keywords: management science process AACSB: Analytical thinking 53) ________ involves determining the functional relationship between variables, parameters, and equations. A) Problem observation B) Problem definition C) Model construction D) Model solution Answer: C Diff: 1 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: management science process, model construction AACSB: Analytical thinking 54) Which steps of the management science process can either be a recommended decision or information that helps a manager make a decision? A) model implementation B) problem definition C) model solution D) problem formulation Answer: C Diff: 2 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: management science process, model solution AACSB: Analytical thinking 10 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 55) The result of an effective decision-making process should be monitored in order to: A) reveal the break-even point. B) reveal errors in the implementation. C) keep fixed and variable costs distinct. D) change the scientific method. Answer: B Diff: 2 Page Ref: 27 Section Heading: The Management Science Approach to Problem Solving Keywords: decision making process AACSB: Analytical thinking 56) Which of these disciplines typically does not fall under the umbrella of analytics? A) information systems B) statistics C) management science D) operations management Answer: D Diff: 2 Page Ref: 27 Section Heading: Management Science and Business Analytics Keywords: big data, analytics AACSB: Application of knowledge 57) The indicator that results in total revenues being equal to total cost is called the: A) marginal cost. B) marginal volume. C) break-even point. D) profit mix. Answer: C Diff: 1 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 58) Variable cost: A) depends on the number of units produced. B) plus marginal cost equals fixed cost. C) is equal to total cost in deterministic models. D) is the same as average cost. Answer: A Diff: 2 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 11 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 59) The components of break-even analysis are: A) cost and profit. B) volume and cost. C) volume, cost and profit. D) volume and profit. Answer: C Diff: 1 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 60) ________ are generally independent of the volume of units produced and sold. A) Fixed costs B) Variable costs C) Profits D) Average cost Answer: A Diff: 1 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 61) The purpose of break-even analysis is to determine the number of units of a product to sell that will: A) appeal to the consumer. B) result in a profit. C) result in a loss. D) result in zero profit. Answer: D Diff: 2 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 62) Variable cost does not include: A) raw materials and resources. B) staff and management salaries. C) material handling and freight. D) direct labor and packaging. Answer: B Diff: 2 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 12 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 63) Which variable is not a component of break-even analysis? A) fixed costs B) variable costs C) number of employees D) number of customers Answer: C Diff: 1 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 64) At the break-even point: A) total revenue equals total cost. B) profit is maximized. C) revenue is maximized. D) costs are minimized. Answer: A Diff: 1 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 65) If the price increases, but fixed and variable costs do not change, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease, depending on sales. Answer: A Diff: 2 Page Ref: 32 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 66) If the price decreases, but fixed and variable costs do not change, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease, depending on sales. Answer: B Diff: 2 Page Ref: 32 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 13 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 67) The term ________ refers to testing how a problem solution reacts to changes in one or more of the model parameters. A) graphical solution B) decision analysis C) sensitivity analysis D) break-even analysis Answer: C Diff: 2 Page Ref: 32 Section Heading: Model Building: Break-Even Analysis Keywords: sensitivity analysis, modeling process AACSB: Analytical thinking 68) If fixed costs decrease, but variable cost and price remain the same, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease depending on sales. Answer: A Diff: 2 Page Ref: 33 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 69) If fixed costs increase, but variable cost and price remain the same, the break-even point: A) decreases. B) increases. C) remains the same. D) may increase or decrease depending on sales. Answer: B Diff: 2 Page Ref: 33 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 70) Administrators at a university will charge students $175 to attend freshman orientation. It costs $10,000 to reserve a room, hire extra security, and bring in a moonwalk. Assume it costs $15 per student for the administrators to provide the course materials. How many students would have to register for orientation for the university to break even? A) 54.25 B) 58 C) 56 D) 62.5 Answer: D Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 14 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 71) A university is planning a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? A) $120 B) $150 C) $175 D) $200 Answer: C Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 72) A university is planning an online seminar. It costs $30 to live stream an instructor from Elbonia. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? A) $55 B) $15 C) $26.50 D) $75.75 Answer: C Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 73) It costs $50,000 to start a production process. Variable cost is $25 per unit and revenue is $45 per unit. What is the break-even point? A) 1000 units B) 1111 units C) 2000 units D) 2500 units Answer: D Diff: 1 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 15 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 74) It costs $6,000 to start a production process. Variable cost is $2 per unit and revenue is $5 per unit. What is the break-even point? A) 1000 units B) 1111 units C) 2000 units D) 2500 units Answer: C Diff: 1 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking Yowzah Bids Yowzah receives bids from four companies we'll call A, B, C, and D to supply product for the coming year. René Descartes, the Yowzah VP of Plotting takes the bids and creates this graph to bring to the next executive meeting. 75) The company with the lowest variable cost is: A) A. B) B. C) C. D) D. Answer: D Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 16 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 76) The company with the highest variable cost is: A) A. B) B. C) C. D) D. Answer: A Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 77) Over the range of demand shown by this graph, which action would completely remove one of the potential suppliers from consideration? A) lowering A's fixed cost by 10% B) raising B's variable cost by 10% C) raising C's variable and fixed costs by 10% D) lowering D's fixed cost by 25% Answer: C Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 78) Which of these changes would have no effect on which supplier is chosen in the output range of 0 units to 20,000 units? A) Variable costs fall 10% for all bidders. B) Fixed costs rise 10% for all bidders. C) Companies A and B swap their figures for fixed costs. D) Companies C and D swap their figures for fixed costs. Answer: B Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 79) Which level of anticipated demand is least sensitive to variations in fixed and variable cost estimates? A) 5,000 B) 10,000 C) 15,000 D) 20,000 Answer: B Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 17 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 80) Company A has a fixed cost of 75,000 and a variable cost of 15. Company B's fixed cost is 90,000 and variable cost is 11. At what point is Yowzah indifferent between the two bidders? A) 3,250 B) 3,500 C) 3,750 D) 4,000 Answer: C Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 81) Yowzah receives a frantic call from company C. Evidently the fixed cost they quoted was in rupees rather than dollars. If the current exchange rate is 60 rupees to the dollar, what is the net effect of an updated analysis? A) Company C is the bidder of choice throughout the range depicted in the graph. B) Company C has the highest total cost throughout the range depicted in the graph. C) Company C has the highest fixed cost of all four companies. D) Even beyond the range depicted in the graph, company C would be the bidder of choice. Answer: A Diff: 1 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 82) Which of the following statements is false? A) Decision models selectively describe the managerial situation. B) Decision models consider all factors from the real world. C) Decision models designate performance measures that reflect objectives. D) Decision models designate decision variables. Answer: B Diff: 2 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: models, decision models, modeling techniques AACSB: Analytical thinking 83) Decision support systems and sensitivity analysis are useful management science tools for answering the question: A) by when? B) who else? C) how much? D) what if? Answer: D Diff: 2 Page Ref: 42 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking 18 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 84) A difficult aspect of using spreadsheets to solve management science problems is: A) obtaining the solution to standard management science problems. B) data entry. C) performing sensitivity analysis. D) setting up a spreadsheet with complex models and formulas. Answer: D Diff: 2 Page Ref: 34 Section Heading: Computer Solution Keywords: computer solution, spreadsheets AACSB: Analytical thinking 85) A technique that assumes certainty in its solution is referred to as: A) stochastic. B) probabilistic. C) deterministic. D) parametric. Answer: C Diff: 2 Page Ref: 38 Section Heading: Management Science Modeling Techniques Keywords: modeling, models, modeling techniques AACSB: Analytical thinking 86) Classification of management science techniques does not recognize: A) linear mathematical programming. B) probabilistic techniques. C) network techniques. D) computer programming. Answer: D Diff: 1 Page Ref: 37 Section Heading: Management Science Modeling Techniques Keywords: management science techniques, classification of techniques AACSB: Analytical thinking 87) Linear mathematical programming techniques assume that all parameters in the models are: A) known with certainty. B) unknown. C) predictable. D) unpredictable. Answer: A Diff: 2 Page Ref: 37 Section Heading: Management Science Modeling Techniques Keywords: management science techniques AACSB: Analytical thinking 19 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 88) Decision analysis is a ________ technique. A) linear mathematical programming B) probabilistic C) network D) non-linear programming technique Answer: B Diff: 1 Page Ref: 38 Section Heading: Management Science Modeling Techniques Keywords: management science techniques AACSB: Analytical thinking 89) Which one of the following techniques is not a mathematical programming technique? A) linear programming models B) transportation models C) analytical hierarchy process D) integer linear programming technique Answer: C Diff: 2 Page Ref: 39 Section Heading: Management Science Modeling Techniques Keywords: management science techniques AACSB: Analytical thinking 90) The analytical hierarchy process is used to: A) convert qualitative problems into quantitative problems B) minimize the number of levels in an organization C) choose among several alternatives D) determine the optimal route between two points Answer: C Diff: 2 Page Ref: 39 Section Heading: Management Science Modeling Techniques Keywords: AHP, analytical hierarchy process AACSB: Analytical thinking 91) Which of these techniques is typically considered part of the operations realm rather than the management science realm? A) forecasting B) queuing C) networks D) routing Answer: A Diff: 2 Page Ref: 39 Section Heading: Management Science Modeling Techniques Keywords: AHP, analytical hierarchy process AACSB: Analytical thinking 20 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 92) Which one of the following management science methods is not a probabilistic technique? A) assignment models B) decision analysis C) queuing analysis D) statistical analysis Answer: A Diff: 2 Page Ref: 39 Section Heading: Management Science Modeling Techniques Keywords: management science techniques AACSB: Analytical thinking 93) A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. The constraint that represents this condition is: A) x1 ≤ 8, x2 ≤ 8, x3 ≤ 8. B) x1 + x2 + x3 ≥ 24. C) x1 + x2 + x3 ≤ 24. D) 4x1 + 3x2 + 2x3 ≤ 24. Answer: D Diff: 3 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints AACSB: Analytical thinking 94) A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. At most, the baker could make: A) 4 batches of bread. B) 2 pounds of muffins. C) 8 batches of cookies. D) 24 pounds of flour. Answer: C Diff: 2 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints AACSB: Analytical thinking 21 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 95) A baker uses organic flour from a local farmer in all of his baked goods. For each batch of bread (x1), he uses 4 pounds of flour. For a batch of cookies (x2), he uses 3 pounds, and for a batch of muffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 pounds per week. Which of these combinations can be made with the available flour? A) 3 batches of bread, 3 batches of cookies, and 3 batches of muffins B) 2 batches of bread, 4 batches of cookies, and 2 batches of muffins C) 3 batches of bread, 4 batches of cookies, and 2 batches of muffins D) 2 batches of bread, 1 batches of cookies, and 1 batches of muffins Answer: B Diff: 2 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints AACSB: Analytical thinking 96) An objective function: A) shows where the break-even point is. B) describes how much of a resource can be used. C) can represent costs or profits. D) describes something to be maximized. Answer: C Diff: 2 Page Ref: 37 Section Heading: Management Science Modeling Techniques Keywords: objective function, model construction AACSB: Analytical thinking 97) Larry's Fish Market buys salmon (S) for $5 per pound and a local whitefish (W) for $3.50 per pound. Larry wants to minimize his cost, but he cannot spend more than $160. The objective function that minimizes these costs for Larry is: A) 5S + 3.5W ≤ 160. B) Min 5S + 3.5 W. C) Max 5S + 3.5 W. D) Min 5S + 3.5W ≥ 160. Answer: B Diff: 3 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: objective function, model construction AACSB: Analytical thinking 22 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 98) It's time to buy pet food again and Lisa heads to the grocery store with $40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs $1 per can and cat food costs $0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is an appropriate objective function for this scenario? A) Min Z = 1D + 0.5C B) Min Z = 2D + 1C C) Min Z = D + C ≤ 40 D) Min Z = D + C ≥ 3 Answer: A Diff: 3 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: objective function AACSB: Analytical thinking 99) It's time to buy pet food again and Lisa heads to the grocery store with $40 in her purse, leaving her seven hungry cats and four hungry dogs at home. Dog food costs $1 per can and cat food costs $0.50 per can. Dogs eat two full cans of food each day but cats eat only one can. Lisa would like to buy enough food to last through her three-day weekend. What is one appropriate constraint for this scenario? A) 7C + 4D ≥ 3 B) 1C + 2D ≤ 40 C) .5C + 1D ≤ 40 D) 7C + 4D ≥ 1.5 Answer: C Diff: 3 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints AACSB: Analytical thinking 100) Marriott used which of the following management science techniques to help improve profit by $120 million over two years? A) optimization, decision analysis, and forecasting B) forecasting, queuing theory, and inventory analysis C) queuing theory, optimization, and inventory analysis D) forecasting, simulation, and optimization Answer: D Diff: 3 Page Ref: 26 Section Heading: The Management Science Approach to Problem Solving Keywords: management science, management scientist AACSB: Analytical thinking 23 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 101) Which of these is a typical attribute of a decision support system? A) interactive B) intranet C) integrated D) insubordinate Answer: A Diff: 1 Page Ref: 41 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking 102) Instantaneous information about business transactions is achievable through the use of: A) point of sale systems and CPM B) point of sale systems and EDI C) decision support systems and EDI D) decision support systems and CPM Answer: B Diff: 2 Page Ref: 42 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking 103) Which of these decision support systems is the most comprehensive with respect to an entire organization? A) an Excel spreadsheet B) an ERP C) QM for Windows D) OLAP Answer: B Diff: 2 Page Ref: 42 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking 104) The relationship d = 5000 - 25p describes what happens to demand (d) as price (p) varies. Price can vary between $10 and $50. How many units can be sold when the price is $10? Answer: 4750 Diff: 2 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: break-even analysis AACSB: Analytical thinking 24 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 105) A production process requires a fixed cost of $50,000 and the variable cost per unit is $25. The revenue per unit was projected to be $45, but a recent marketing study shows that because of an emerging competitor, the revenue will be about 12% lower. How does this affect the breakeven point? Answer: The break-even point will be higher, at 3424 units, which is a 37% increase. Diff: 3 Page Ref: 32 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 106) Administrators at a university are planning to offer a summer seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? Answer: $175 Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 107) A newly opened bed-and-breakfast projects the following: Monthly fixed costs $8000 Variable cost per occupied room per night $40 Revenue per occupied room per night $165 Write the expression for total cost per month. Answer: C(x) = 8000 9 40x Diff: 2 Page Ref: 28 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 108) A newly opened bed-and-breakfast projects the following: Monthly fixed costs $8000 Variable cost per occupied room per night $40 Revenue per occupied room per night $165 Write the expression for total revenue per month. Answer: R(x) = 165x Diff: 2 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 25 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 109) A newly opened bed-and-breakfast projects the following: Monthly fixed costs $8000 Variable cost per occupied room per night $40 Revenue per occupied room per night $165 How many rooms would have to be occupied per month in order to break even? Answer: 64 rooms Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 110) Aaron decides to rent out a spare bedroom on a part time basis for weary business travelers coming to his fair city. Aaron's bed-and-breakfast projects the following: Monthly fixed costs $2000 Variable cost per occupied room per night $10 Revenue per occupied room per night $165 How many nights would the room have to be occupied per month in order to break even? Answer: 12.90 nights Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 111) A script writer has received an advance against royalties of $10,000. The royalty rate is $2 for every performance in the United States, and $3 for every performance outside the United States. Define variables for this problem. Answer: x = # of performances in the United States y = # of performances outside the United States Diff: 3 Page Ref: 23 Section Heading: The Management Science Approach to Problem Solving Keywords: break-even analysis AACSB: Analytical thinking 112) A business analyst describes his company's profit function as 3x2 + 6x - 200. If x is the output volume, what statements can you make about the price, fixed cost, and variable cost? Answer: The fixed cost is $200, but we can't determine exactly what the price and variable cost are. Diff: 3 Page Ref: 29 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis, variable definition AACSB: Analytical thinking 26 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 113) A script writer has received an advance against royalties of $10,000. The royalty rate is $2 for every performance in the United States, and $3 for every performance outside the United States. Write an expression that could be used to compute the number of performances in order to cover the advance. Answer: 10000 = 2x + 3y Diff: 3 Page Ref: 25 Section Heading: The Management Science Approach to Problem Solving Keywords: break-even analysis AACSB: Analytical thinking 114) Students are organizing a "Battle of the Bands" contest. They know that at least 100 people will attend. The rental fee for the hall is $150 and the winning band will receive $500. In order to guarantee that they break even, how much should they charge for each ticket? Answer: $6.50 Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 115) A popular performer is scheduled to appear at a major city. The promoter is deciding between two venues, the larger of which costs $20,000 to rent and the smaller of which costs $12,000 to rent. Ticket prices for the smaller venue are $20, but the promoter is unsure what to charge per ticket for the larger venue. If exactly 1000 customers arrive, what percentage change in ticket prices would make the profit at the large venue identical to that of the smaller venue? Answer: Increase 40% Diff: 3 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 116) Administrators at a university will charge students $250 to attend freshman orientation. It costs $8,000 to reserve their grand ballroom, hire extra security, and bring in a moonwalk. Assume it costs $10 per student for the administrators to provide the course materials. How many students would have to register for orientation for the university to break even? Answer: 33.3 Diff: 2 Page Ref: 30 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 27 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 117) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is $6 from cooperative A and $5.50 per unit from cooperative B. Define variables that would tell how many units to purchase from each source. Answer: X1 = # of units from cooperative A X2 = # of units from cooperative B Diff: 3 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: break-even analysis, variable definition AACSB: Analytical thinking 118) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is $6 from cooperative A and $5.50 per unit from cooperative B. Develop an objective function that would minimize the total cost. Answer: Min 6x1 + 5.5x2 Diff: 3 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: objective function, break-even analysis, model development AACSB: Analytical thinking 119) A manufacturer buys peas for vegetable pies from two cooperatives. The price per unit is $6 from cooperative A and $5.50 per unit from cooperative B. The manufacturer needs at least 12,000 units of peas. Cooperative A can supply up to 8000 units, and cooperative B can supply at least 6000 units. Develop constraints for these conditions. Answer: XA + XB ≥ 12000 XA ≤ 8000 XB ≥ 6000 Diff: 3 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints, model development AACSB: Analytical thinking 120) A group of professors struggles to craft a set of assessment questions for their operations management intro class. They want to cover four topic areas with at least four questions each and have no more than twenty questions total for the assessment. What would a set of constraints look like if they chose an optimization approach to the assessment? Answer: X1 ≥ 4 X2 ≥ 4 X3 ≥ 4 X4 ≥ 4 X1 + X2 + X3 + X4 ≤ 20 Diff: 3 Page Ref: 25 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints AACSB: Analytical thinking 28 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 121) What are some different types of decision support systems? Answer: A DSS can be small and singular, such as an Excel spreadsheet set up for a single user to solve a specific type of problem. A DSS can also be large and complex, linking many users and databases. The DSS can be a data-oriented system or a model-oriented system. Some decision support systems (ERP systems) help managers make decisions about all facets of a company's operations. Diff: 2 Page Ref: 42 Section Heading: Management Science Models in Decision Support Systems Keywords: decision support systems AACSB: Analytical thinking 122) A manager of the cereal bar at the college campus has determined that the profit made for each bowl of Morning Buzz cereal sold, x, is equal to: Z = $4x - 0.5x. Each bowl of Morning Buzz weighs 6 ounces, and the manager has 12 lbs (192 ounces) of cereal available each day, which can be written as the constraint, 6x ≤ 192. What maximum profit will be made from Morning Buzz if it is all sold in one day? Answer: $112 Diff: 2 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: model development AACSB: Analytical thinking 123) The College Coffee Cafe buys tea from three suppliers. The price per pound is $15.00 from supplier A, $17.50 from supplier B, and $21.00 from supplier C. They have budgeted $175 to purchase the tea. The cafe needs at least 12 pounds of tea, and supplier C can supply no more than 4 pounds. Develop constraints for these conditions. Answer: 15.00 XA + 17.50 XB + 21 XC ≤ 175 XA + XB + XC ≥ 12 XC ≤ 4 Diff: 3 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: constraints, model development AACSB: Analytical thinking 124) The College Coffee Cafe receives a profit of $1.25 for each cup of house tea that they sell, $1.40 for each cup of the premium brand, and $1.50 for each cup of their special blend. Develop an objective that maximizes profit. Answer: Max 1.25x1 + 1.40x2 + 1.50x3 Diff: 2 Page Ref: 24 Section Heading: The Management Science Approach to Problem Solving Keywords: objective function, model development AACSB: Analytical thinking 29 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Yowzah Bids Yowzah receives bids from four companies we'll call A, B, C, and D to supply product for the coming year. René Descartes, the Yowzah VP of Plotting takes the bids and creates this graph to bring to the next executive meeting. 125) Describe a general approach for determining the variable cost of any of the companies in this plot. Answer: The variable cost is reflected by the slope, so a rise over run formulation can be used. The leftmost edge of the graph represents x = 0 and the rightmost is a value of 20,000, which is a difference of 20,000. By subtracting the leftmost y-coordinate from each line from the rightmost, the rise can be computed. Then dividing the rise, or ∆y, by the run, ∆x, to determine the variable cost. Diff: 2 Page Ref: 31 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 126) Which of the companies has the greatest variable cost? Answer: The variable cost is reflected by the slope, and the line representing company A starts lower than the others on the left side of the graph and ends higher than all others, thus it must have the greatest slope and therefore highest variable cost. Diff: 1 Page Ref: 31 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 30 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 127) What is the point of indifference between company A and company C? How does this point of indifference affect Yowzah's decision? Answer: Company A appears to have a fixed cost of 75,000 and company C appears to have a fixed cost of 160,000. The variable cost (slope) for company A is (375,000 - 75,000)/20,000 = 15. The variable cost (slope) for company C is (280,000 - 160,000)/20,000 = 6. The point of indifference can be found by setting the two lines equal to each other, so 75,000 + 15x = 160,000 + 6x; 9x = 85,000; x = 9444.4 The point of indifference doesn't affect Yowzah's decision in this range as both companies have higher costs than their fierce rival company B around this range of output. Diff: 1 Page Ref: 31 Section Heading: Model Building: Break-Even Analysis Keywords: break-even analysis AACSB: Analytical thinking 31 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Introduction to Management Science, 13e, Global Edition (Taylor) Chapter 2 Linear Programming: Model Formulation and Graphical Solution 1) Linear programming is a model consisting of linear relationships representing a firm's decisions given an objective and resource constraints. Answer: TRUE Diff: 2 Page Ref: 54 Section Heading: Model Formulation Keywords: model formulation AACSB: Analytical thinking 2) The objective function always consists of either maximizing or minimizing some value. Answer: TRUE Diff: 2 Page Ref: 54 Section Heading: Model Formulation Keywords: objective function AACSB: Analytical thinking 3) The objective function is a linear relationship reflecting the objective of an operation. Answer: TRUE Diff: 1 Page Ref: 54 Section Heading: Model Formulation Keywords: model formulation AACSB: Analytical thinking 4) Both objective functions and constraints contain parameters. Answer: TRUE Diff: 2 Page Ref: 54 Section Heading: Model Formulation Keywords: model formulation AACSB: Analytical thinking 5) Proportionality means the slope of a constraint is proportional to the slope of the objective function. Answer: FALSE Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models, proportionality AACSB: Analytical thinking 6) The terms in the objective function or constraints are additive. Answer: TRUE Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models, additive AACSB: Analytical thinking 1 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 7) The terms in the objective function or constraints are multiplicative. Answer: FALSE Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models, additive AACSB: Analytical thinking 8) All linear programming models exhibit a set of constraints. Answer: TRUE Diff: 1 Page Ref: 54 Section Heading: Model Formulation Keywords: properties of linear programming models, constraints AACSB: Analytical thinking 9) When using the graphical method, only one of the four quadrants of an xy-axis needs to be drawn. Answer: TRUE Diff: 1 Page Ref: 59 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical linear programming AACSB: Analytical thinking 10) Linear programming models exhibit linearity among all constraint relationships and the objective function. Answer: TRUE Diff: 1 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear prog models, linearity, proportionality AACSB: Analytical thinking 11) The equation 8xy = 32 satisfies the proportionality property of linear programming. Answer: FALSE Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: graphical solution, proportionality AACSB: Analytical thinking 12) Typically, finding a corner point for the feasible region involves solving a set of three simultaneous equations. Answer: FALSE Diff: 2 Page Ref: 65 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, extreme points, feasible region AACSB: Analytical thinking 2 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 13) Objective functions in linear programs always minimize costs. Answer: FALSE Diff: 2 Page Ref: 54 Section Heading: Model Formulation Keywords: properties of linear programming models, objective function AACSB: Analytical thinking 14) The feasible solution area contains infinite solutions to the linear program. Answer: TRUE Diff: 1 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: properties of linear programming models, feasible solution area AACSB: Analytical thinking 15) There is exactly one optimal solution point to a linear program. Answer: FALSE Diff: 2 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: properties of linear programming models, optimal solution point AACSB: Analytical thinking 16) The following equation represents a resource constraint for a maximization problem: X + Y ≥ 20. Answer: FALSE Diff: 2 Page Ref: 56 Section Heading: A Maximization Model Example Keywords: properties of linear programming models, constraints AACSB: Analytical thinking 17) The optimal solution for a graphical linear programming problem is the corner point that is the farthest from the origin. Answer: FALSE Diff: 2 Page Ref: 62 Section Heading: Graphical Solutions of Linear Programming Models Keywords: feasibility, constraints AACSB: Analytical thinking 18) A minimization model of a linear program contains only surplus variables. Answer: FALSE Diff: 1 Page Ref: 75 Section Heading: A Minimization Model Example Keywords: properties of linear programming models, surplus variables AACSB: Analytical thinking 3 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 19) In the graphical approach, simultaneous equations may be used to solve for the optimal solution point. Answer: TRUE Diff: 2 Page Ref: 65 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking 20) Slack variables are only associated with maximization problems. Answer: FALSE Diff: 2 Page Ref: 67 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, slack variables AACSB: Analytical thinking 21) Surplus variables are only associated with minimization problems. Answer: FALSE Diff: 2 Page Ref: 75 Section Heading: A Minimization Model Example Keywords: graphical solution, surplus variable AACSB: Analytical thinking 22) If the objective function is parallel to a constraint, the constraint is infeasible. Answer: FALSE Diff: 2 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solution AACSB: Analytical thinking 23) Multiple optimal solutions occur when constraints are parallel to each other. Answer: FALSE Diff: 2 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solution AACSB: Analytical thinking 24) Graphical solutions to linear programming problems have an infinite number of possible objective function lines. Answer: TRUE Diff: 2 Page Ref: 62 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, objective function line AACSB: Analytical thinking 4 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 25) The first step in formulating a linear programming model is to define the objective function. Answer: FALSE Diff: 2 Page Ref: 54 Section Heading: Introduction Keywords: linear programming problems, formulation AACSB: Analytical thinking 26) A linear programming problem requires a choice between alternative courses of action. Answer: TRUE Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming problems, formulation AACSB: Application of knowledge 27) The term continuous is synonymous with divisible in the context of linear programming. Answer: TRUE Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming problems, formulation AACSB: Application of knowledge 28) Linear programming problems can model decreasing marginal returns. Answer: FALSE Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming problems, formulation AACSB: Application of knowledge 29) One of the most frequent objectives of business forms is to gain the most profit possible. Answer: TRUE Diff: 1 Page Ref: 56 Section Heading: Introduction Keywords: linear programming problems, maximization AACSB: Analytical thinking 30) We have George Dantzig to thank for developing linear programming. Answer: TRUE Diff: 2 Page Ref: 57 Section Heading: A Maximization Model Example Keywords: linear programming, Dantzig AACSB: Analytical thinking 5 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 31) In the absence of nonnegativity constraints, our solution cannot have zero values for decision variables. Answer: FALSE Diff: 2 Page Ref: 57 Section Heading: A Maximization Model Example Keywords: nonnegativity, linear programming AACSB: Analytical thinking 32) If there are no feasible solutions to a linear programming model, then the best course of action for a manager is to choose a solution that violates at least one constraint. Answer: FALSE Diff: 1 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: properties of linear programming models, feasible solution area AACSB: Analytical thinking 33) ________ are mathematical symbols representing levels of activity. Answer: Decision variables Diff: 1 Page Ref: 54 Section Heading: Model Formulation Keywords: decision variables, model formulation AACSB: Analytical thinking 34) A(n) ________ is a linear relationship representing a restriction on decision making. Answer: constraint Diff: 1 Page Ref: 54 Section Heading: Model Formulation Keywords: constraint, model formulation AACSB: Analytical thinking 35) If at least one constraint in a linear programming model is violated, the solution is said to be ________. Answer: infeasible Diff: 1 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: constraint, infeasible solution AACSB: Analytical thinking 36) A graphical solution is limited to solving linear programming problems with ________ decision variables. Answer: two Diff: 1 Page Ref: 58 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking 6 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 37) The ________ solution area is an area bounded by the constraint equations. Answer: feasible Diff: 1 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking 38) Multiple optimal solutions can occur when the objective function line is ________ to a constraint line. Answer: parallel Diff: 2 Page Ref: 67 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, multiple optimal solutions AACSB: Analytical thinking 39) XY Corporation makes two products, X and Y, and uses graphical linear programming to determine their monthly product mix. This November, their only production constraint is X ≤ 75. November's production problem is ________. Answer: unbounded Diff: 2 Page Ref: 78 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solution, unbounded problem AACSB: Analytical thinking 40) The best feasible solution is ________. Answer: optimal Diff: 1 Page Ref: 63 Section Heading: Graphical Solutions of Linear Programming Models Keywords: optimal solutions AACSB: Analytical thinking 41) In a constraint, the ________ variable represents unused resources. Answer: slack Diff: 1 Page Ref: 67 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, surplus variable AACSB: Analytical thinking 42) ________ is the difference between the left- and right-hand sides of a greater than or equal to constraint. Answer: Surplus Diff: 1 Page Ref: 75 Section Heading: A Minimization Model Example Keywords: surplus AACSB: Analytical thinking 7 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 43) If the objective function is parallel to a constraint, the linear program could have ________. Answer: multiple optimal solutions Diff: 2 Page Ref: 67 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solutions, multiple optimal solutions AACSB: Analytical thinking 44) Corner points on the boundary of the feasible solution area are called ________ points. Answer: extreme Diff: 1 Page Ref: 64 Section Heading: Graphical Solutions of Linear Programming Models Keywords: feasibility, constraints AACSB: Analytical thinking 45) ________ are at the endpoints of the constraint line segment that the objective function parallels. Answer: Alternate optimal solutions Diff: 3 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: alternative optimal solutions, multiple optimal solutions AACSB: Analytical thinking 46) The ________ step in formulating a linear programming model is to define the decision variables. Answer: first Diff: 1 Page Ref: 56 Section Heading: A Maximization Model Example Keywords: linear programming, formulation AACSB: Analytical thinking 47) The management scientist constructed a linear program to help the alchemist maximize his gold production process. The computer model chugged away for a few minutes and returned an answer of infinite profit., which is what might be expected from a(n) ________ problem. Answer: unbounded Diff: 1 Page Ref: 78 Section Heading: Irregular Types of Linear Programming Problems Keywords: unbounded AACSB: Analytical thinking 48) The ________ property of linear programming models indicates that the rate of change, or slope, of the objective function or a constraint is constant. Answer: proportionality or linearity Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models, certainty AACSB: Analytical thinking 8 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 49) The objective function 3x + 2y + 4xy violates the assumption of ________. Answer: additivity Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming properties AACSB: Application of knowledge 50) Mildred is attempting to prepare an optimal quantity of macaroni and cheese for the potluck supper this Sunday. The instructions indicate that one cup of water is needed for each box she needs to prepare. She sleeps well on Saturday night, secure in her knowledge that she knows the precise amount of water she will need the next day. This knowledge illustrates the assumption of ________. Answer: certainty Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming properties AACSB: Application of knowledge 51) Tim! airlines procurement division works with their linear programming algorithm to secure contracts for gasoline for the coming year. After twenty minutes of thinking, the computer suggests that they secure 425.8125 contracts with their suppliers. This value illustrates the assumption of ________ in linear programming models. Answer: divisibility or continuous Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming properties AACSB: Application of knowledge 52) In a linear programming problem, the binding constraints for the optimal solution are: 5x1 + 3x2 ≤ 30 2x1 + 5x2 ≤ 20 As long as the slope of the objective function stays between ________ and ________, the current optimal solution point will remain optimal. Answer: -5/3, -2/5 Diff: 3 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: optimal solution, solution interpretation, slope AACSB: Analytical thinking 9 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 53) In a graphical approach to a linear programming problem, the objective function is represented by a(n) ________. Answer: (straight) line Diff: 2 Page Ref: 62 Section Heading: Graphical Solutions of Linear Programming Models Keywords: optimal solution, solution interpretation, slope AACSB: Analytical thinking 54) In a graphical approach to a linear programming problem, the objective function has a maximum value when it is ________ the origin. Answer: farthest away from Diff: 2 Page Ref: 65 Section Heading: Graphical Solutions of Linear Programming Models Keywords: optimal solution, solution interpretation, slope AACSB: Analytical thinking 55) The three types of linear programming constraints are ________, ________, and ________. Answer: ≥, ≤, = (greater than or equal to, less than or equal to, equal to) Diff: 1 Page Ref: 72 Section Heading: A Minimization Model Example Keywords: linear programming, constraint AACSB: Analytical thinking 56) In a linear programming problem, the binding constraints for the optimal solution are: 5x1 + 3x2 ≤ 30 2x1 + 5x2 ≤ 20 Which of these objective functions will lead to the same optimal solution? A) 2x1 + 1x2 B) 7x1 + 8x2 C) 80x1 + 60x2 D) 25x1 + 15x2 Answer: D Diff: 3 Page Ref: 62 Section Heading: Graphical Solutions of Linear Programming Models Keywords: optimal solution, solution interpretation, slope AACSB: Analytical thinking 10 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 57) Decision variables: A) measure the objective function. B) measure how much or how many items to produce, purchase, hire, etc. C) always exist for each constraint. D) measure the values of each constraint. Answer: B Diff: 2 Page Ref: 54 Section Heading: Model Formulation Keywords: decision variables AACSB: Analytical thinking 58) In a linear programming problem, a valid objective function can be represented as: A) Max Z = 5xy B) Max Z 5x2 + 2y2 C) Max 3x + 3y + 1/3 z D) Min (x1 + x2) / x3 Answer: C Diff: 3 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: objective function AACSB: Analytical thinking 59) Which of the following could not be a linear programming problem constraint? A) 1A + 2B ≠ 3 B) 1A + 2B = 3 C) 1A + 2B ≤ 3 D) 1A + 2B ≥ 3 Answer: A Diff: 2 Page Ref: 56 Section Heading: A Maximization Model Example Keywords: formulation, constraints AACSB: Analytical thinking 60) Which of the following could be a linear programming objective function? A) Z = 1A + 2BC + 3D B) Z = 1A + 2B + 3C + 4D C) Z = 1A + 2B / C + 3D D) Z = 1A + 2B2 + 3D Answer: B Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: objective function AACSB: Analytical thinking 11 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 The campaign manager for a doomed candidate is considering the which states to visit during the last frenzied campaign week leading up to the nationwide election. Pennsylvania (P), Wisconsin (W), Florida (F), New York (Y), and North Carolina (C) are all aching for one last visit, but the candidate has only 80 hours and $250 million left in her campaign fund. A visit to Pennsylvania takes 10 hours and costs $15 million but earns 1% of the electorate. A visit to Wisconsin takes 15 hours and costs $20 million and earns 1.5%; a visit to Florida is only $8 million but takes 16 hours and earns 2%, and a visit to New York costs $25 million, requires 2 hours and earns 2% of the electorate. North Carolina requires 18 hours and $22 million per trip but earns 3% of the electorate. 61) What is the objective function? A) MIN 10P+15W+16F+2Y+18C B) MAX 10P+15W+16F+2Y+18C C) MIN 15P+20W+8F+25Y+22C D) MAX P+1.5W+2F+2Y+3C Answer: D Diff: 2 Page Ref: 56 Section Heading: A Maximization Model Example Keywords: formulation, objective function AACSB: Analytical thinking 62) What is the time constraint? A) P+1.5W+2F+2Y+3C ≤ 250 B) P+1.5W+2F+2Y+3C ≤ 80 C) 10P+15W+16F+2Y+18C ≤ 80 D) 15P+20W+8F+25Y+22C ≤ 80 Answer: C Diff: 2 Page Ref: 56 Section Heading: A Maximization Model Example Keywords: formulation, constraints AACSB: Analytical thinking 63) What is the financial constraint? A) P+1.5W+2F+2Y+3C ≤ 250 B) 15P+20W+8F+25Y+22C ≤ 250 C) 15P+20W+8F+25Y+22C ≤ 80 D) 10P+15W+16F+2Y+18C ≤ 250 Answer: B Diff: 2 Page Ref: 56 Section Heading: A Maximization Model Example Keywords: formulation, constraints AACSB: Analytical thinking 12 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 64) The ________ property of linear programming models indicates that the rate of change or slope of the objective function or a constraint is constant. A) additive B) divisibility C) certainty D) proportionality Answer: D Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models AACSB: Analytical thinking 65) The ________ property of linear programming models indicates that the values of all the model parameters are known and are assumed to be constant. A) additive B) divisibility C) certainty D) proportionality Answer: C Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: properties of linear programming models AACSB: Analytical thinking 66) The region that satisfies all of the constraints in a graphical linear programming problem is called the: A) region of optimality. B) feasible solution space. C) region of non-negativity. D) optimal solution space. Answer: B Diff: 1 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, feasibility AACSB: Analytical thinking 67) In the formulation of a ≥ constraint: A) a surplus variable is subtracted. B) a surplus variable is added. C) a slack variable is subtracted. D) a slack variable is added. Answer: A Diff: 1 Page Ref: 75 Section Heading: A Minimization Model Example Keywords: surplus AACSB: Analytical thinking 13 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 68) Which of the following statements is not true? A) An infeasible solution violates all constraints. B) A feasible solution point does not have to lie on the boundary of the feasible solution. C) A feasible solution satisfies all constraints. D) An optimal solution satisfies all constraints. Answer: A Diff: 2 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, feasibility AACSB: Analytical thinking 69) A hot dog manufacturer wishes to minimize the cost in dollars of producing a low-cost niched product while meeting the dietary guidelines for protein and sodium. Once the model has been run, the surplus variable in the sodium constraint has a value of 1300 milligrams. The best interpretation of this outcome is: A) the value of the sodium in a hot dog is 1300. B) the amount of sodium in a single hot dog should be 1300 milligrams. C) the minimum cost hot dog has 1300 milligrams more sodium than required. D) a hot dog should have at least 1300 milligrams of sodium. Answer: C Diff: 2 Page Ref: 75 Section Heading: A Minimization Model Example Keywords: surplus AACSB: Analytical thinking 70) Which of these statements is best? A) An unbounded problem is also infeasible. B) An infeasible problem is also unbounded. C) An unbounded problem has feasible solutions. D) An infeasible problem has unbounded solutions. Answer: C Diff: 2 Page Ref: 78 Section Heading: Irregular Types of Linear Programming Problems Keywords: infeasible problem, infeasible solution AACSB: Analytical thinking 71) The optimal solution to a linear programming model that has been solved using the graphical approach: A) is typically located at the origin. B) must be below and on the left side of all constraint lines. C) must be above and the right of all constraint lines. D) is typically at some corner of the feasible region. Answer: D Diff: 1 Page Ref: 62 Section Heading: Graphical Solutions of Linear Programming Models Keywords: solution AACSB: Analytical thinking 14 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 72) Without satisfying the non-negativity constraint, a solution that satisfies all the other constraints of a linear programming problem is called: A) feasible. B) infeasible. C) semi-feasible. D) optimal. Answer: B Diff: 3 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, feasibility AACSB: Analytical thinking 73) An intern sets up a linear program to optimize the use of paper products in the men's washroom. The system of equations he develops is: Max 2T + 3S + 4ST s.t 3T + 6S ≤ 40 10T + 10S ≤ 66 10T + 15S ≤ 99 His mentor studies the model, frowns, and admonishes the intern for violating which of the following properties of linear programming models? A) divisibility B) proportionality C) certainty D) additivity Answer: D Diff: 1 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: additivity AACSB: Analytical thinking 74) Which of the following is not a typical characteristic of a linear programming problem? A) Restrictions exist. B) A choice among alternatives is required. C) The problem can be solved graphically. D) The problem has an objective. Answer: C Diff: 1 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: graphical solution AACSB: Analytical thinking 15 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 The campaign manager for a doomed candidate is considering the which states to visit during the last frenzied campaign week leading up to the nationwide election. Pennsylvania (P), Wisconsin (W), Florida (F), New York (Y), and North Carolina (C) are all aching for one last visit, but the candidate has only 80 hours and $250 million left in her campaign fund. A visit to Pennsylvania takes 10 hours and costs $15 million but earns 1% of the electorate. A visit to Wisconsin takes 15 hours and costs $20 million and earns 1.5%; a visit to Florida is only $8 million but takes 16 hours and earns 2%, and a visit to New York costs $25 million, requires 2 hours and earns 2% of the electorate. North Carolina requires 18 hours and $22 million per trip but earns 3% of the electorate. 75) Which of the following is not a feasible schedule? A) two trips each to Pennsylvania and Wisconsin and one trip each to Florida, New York, and North Carolina B) four trips each to New York and North Carolina C) two trips each to Pennsylvania and North Carolina and one trip to Florida D) four trips to Wisconsin and five trips to New York Answer: A Diff: 3 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, feasibility AACSB: Analytical thinking 76) What is the total percentage increase if the candidate makes the following schedule? A) 10% B) 11% C) 12% D) 13% Answer: D Diff: 2 Page Ref: 64 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking 77) ________ is used to analyze changes in model parameters. A) Optimal solution B) Feasible solution C) Sensitivity analysis D) A slack variable Answer: C Diff: 2 Page Ref: 67 Section Heading: Graphical Solutions of Linear Programming Models Keywords: sensitivity analysis AACSB: Analytical thinking 16 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Lame Example Furniture Company makes two products for its adoring public: chairs (C)and tables (T). Each chair requires 5 hours of labor (L) and 4 linear feet of rich mahogany (M), and each table requires 3 hours of labor and 20 linear feet of rich mahogany. The company has 240 labor hours available this week, and the warehouse has 700 linear feet of rich mahogany available. Profit for each chair is $300 and for each table is $1500. 78) Which of the following is not a feasible production plan? A) 35 chairs and 20 tables B) 20 chairs and 35 tables C) 25 chairs and 30 tables D) 30 chairs and 25 tables Answer: B Diff: 3 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: formulation, feasibility AACSB: Analytical thinking 79) What is the maximum profit? A) $52,500 B) $48,000 C) $55,000 D) $56,250 Answer: A Diff: 3 Page Ref: 63 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking 80) In order to maximize profit, how many tables and how many chairs should be produced? A) T = 35, C = 0 B) T = 0, C = 48 C) T = 26.3, C = 32.8 D) T = 28.9, C = 30.7 Answer: A Diff: 3 Page Ref: 63 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking 17 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 81) The theoretical limit on the number of constraints that can be handled by a linear programming problem is: A) 2. B) 3. C) 4. D) unlimited. Answer: D Diff: 1 Page Ref: 54 Section Heading: Model Formulation Keywords: constraints AACSB: Analytical thinking 82) Consider the following maximization problem. MAX z = x + 2y s.t. 2x + 3y ≤ 6 5x + 6y ≤ 30 y≥1 The optimal solution: A) occurs where x = 4.67 and y = 1.11. B) occurs where x = 0 and y = 2. C) occurs where x = 6 and y = 0. D) results in an objective function value of 12. Answer: B Diff: 1 Page Ref: 64 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, extreme points, feasible region AACSB: Analytical thinking 18 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Figure 1: The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. 83) This linear programming problem shown in Figure 1 is a(n): A) maximization problem. B) minimization problem. C) irregular problem. D) cannot tell from the information given Answer: B Diff: 1 Page Ref: 72 Section Heading: A Minimization Model Example Keywords: graphical solution AACSB: Analytical thinking 84) The equation for constraint DH as shown in Figure 1 is: A) 4X + 8Y ≥ 32. B) 8X + 4Y ≥ 32. C) X + 2Y ≥ 8. D) 2X + Y ≥ 8. Answer: C Diff: 3 Page Ref: 72 Section Heading: A Minimization Model Example Keywords: graphical solution, constraints AACSB: Analytical thinking 19 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 85) Which of the following points is not feasible for the graph shown in Figure 1? A) A B) B C) H D) G Answer: D Diff: 1 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, feasible point AACSB: Analytical thinking 86) Which line in Figure 1 is represented by the equation 2X + Y ≥ 8? A) BF B) CG C) DH D) AJ Answer: A Diff: 2 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, constraints AACSB: Analytical thinking 87) Which of the following constraints shown in Figure 1 has a surplus greater than 0? A) BF B) CG C) DH D) AJ Answer: C Diff: 2 Page Ref: 75 Section Heading: A Minimization Model Example Keywords: graphical solution, constraints AACSB: Analytical thinking 88) In Figure 1, the constraint AJ: A) is a binding constraint. B) has no surplus. C) does not contain feasible points. D) contains the optimal solution. Answer: B Diff: 3 Page Ref: 75 Section Heading: A Minimization Model Example Keywords: graphical solution, constraints AACSB: Analytical thinking 20 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Figure 2 89) Consider the optimization problem represented by the graph in Figure 2. Which of the following statements is best? A) This is a maximization problem with a feasible solution. B) This is a maximization problem with no feasible solution. C) This is a minimization problem with a feasible solution. D) This is a minimization problem with no feasible solution. Answer: C Diff: 1 Page Ref: 76 Section Heading: A Minimization Model Example Keywords: graphical solution, feasibility AACSB: Analytical thinking 90) Line segment GH in Figure 2 represents the objective function. Which constraint has surplus? A) AB B) CD C) EF D) none of the constraints has surplus Answer: A Diff: 2 Page Ref: 75 Section Heading: A Minimization Model Example Keywords: graphical solution, surplus variable AACSB: Analytical thinking 21 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 91) What is the equation for the constraint AB shown in Figure 2? A) 3X + 12Y ≥ 15 B) X + 4Y ≥ 12 C) X + Y ≥ 15 D) 12X + 3Y ≥ 36 Answer: D Diff: 3 Page Ref: 73 Section Heading: A Minimization Model Example Keywords: graphical solution, constraints AACSB: Analytical thinking 92) What is the equation for constraint EF shown in Figure 2? A) 4X + 8Y ≥ 64 B) 4X + 8Y ≥ 12 C) 16X + 8Y ≥ 24 D) 16X + 8Y ≥ 32 Answer: A Diff: 3 Page Ref: 73 Section Heading: A Minimization Model Example Keywords: graphical solution, constraints AACSB: Analytical thinking 93) Consider the optimization problem represented by the graph in Figure 2. The objective function is represented by line GH. Where is the optimal solution? A) the intersection of lines AB and EF B) the intersection of lines AB and CD C) the intersection of lines CD and EF D) the upper right corner of the shaded region Answer: C Diff: 1 Page Ref: 73 Section Heading: A Minimization Model Example Keywords: graphical solution, objective function line AACSB: Analytical thinking 94) Consider the optimization problem represented by the graph in Figure 2. Line GH represents the objective function. Which of the following statements is best? A) This is a single optimal solution. B) All points along GH are optimal. C) All points on lines AB, CD and DE that touch the shaded region are optimal. D) All points in the shaded region are optimal Answer: A Diff: 1 Page Ref: 73 Section Heading: A Minimization Model Example Keywords: graphical solution, multiple optimal solutions AACSB: Analytical thinking 22 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 95) In order for an optimization problem to have multiple optimal solutions: A) the objective function and one constraint must have the same y-intercept. B) the objective function and one constraint must have the same slope. C) two or more of the constraints must not have intersection points. D) two or more of the constraints must have the same slope. Answer: B Diff: 2 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solutions, multiple optimal solutions AACSB: Analytical thinking 96) An optimization problem that has multiple optimal solutions: A) means that there are actually no optimal solutions. B) is reflected by the entire feasible region being optimal C) means that the surplus for a third constraint cannot be calculated. D) provides the decision-maker with increased flexibility. Answer: D Diff: 2 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solutions, multiple optimal solutions AACSB: Analytical thinking 97) How would multiple optimal solutions typically appear on a graphical solution? A) a point B) a line C) a plane D) a cube Answer: B Diff: 2 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solutions, multiple optimal solutions AACSB: Analytical thinking 98) Which of the following statements about infeasible problems is best? A) All of the possible solutions violate at least one constraint. B) All of the possible solutions violate all of the constraints. C) At least one of the possible solutions violates all of the constraints. D) At least one of the possible solutions violates at least one of the constraints. Answer: A Diff: 1 Page Ref: 78 Section Heading: Irregular Types of Linear Programming Problems Keywords: infeasible problem, infeasible solution AACSB: Analytical thinking 23 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 99) Greg, a young entrepreneur, has developed an aggressive business plan and is presenting his profit projections on the popular show Shark Tank in hopes of securing some venture capital. He concludes his presentation with an LP model of his planned product mix, and is convinced he will seal the deal by demonstrating that his profits are limitless since his LP model is unbounded. What should the sharks tell him? A) "Limitless profits sound fantastic, here's a blank check." B) "Limitless profits are possible only in minimization models, and we want you to maximize profits." C) "Unlimited profits aren't possible. You must have made a mistake in your LP model." D) "Limitless profits are possible only in maximization models, and we want you to minimize profits." Answer: C Diff: 1 Page Ref: 78 Section Heading: Irregular Types of Linear Programming Problems Keywords: unbounded AACSB: Analytical thinking 100) Multiple optimal solutions can occur when the objective function is ________ a constraint line. A) unequal to B) equal to C) perpendicular to D) parallel to Answer: D Diff: 2 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: irregular types of linear programming problems AACSB: Analytical thinking 101) A slack variable: A) is the amount by which the left side of a ≥= constraint is larger than the right side. B) is the amount by which the left side of a ≤= constraint is smaller than the right side. C) is the difference between the left and right side of a constraint. D) exists for each variable in a linear programming problem. Answer: B Diff: 2 Page Ref: 66 Section Heading: Slack Variables Keywords: slack variables AACSB: Analytical thinking 24 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 The campaign manager for a doomed candidate is considering the which states to visit during the last frenzied campaign week leading up to the nationwide election. Pennsylvania (P), Wisconsin (W), Florida (F), New York (Y), and North Carolina (C) are all aching for one last visit, but the candidate has only 80 hours and $250 million left in her campaign fund. A visit to Pennsylvania takes 10 hours and costs $15 million but earns 1% of the electorate. A visit to Wisconsin takes 15 hours and costs $20 million and earns 1.5%; a visit to Florida is only $8 million but takes 16 hours and earns 2%, and a visit to New York costs $25 million, requires 2 hours and earns 2% of the electorate. North Carolina requires 18 hours and $22 million per trip but earns 3% of the electorate. 102) The campaign manager elects to take one trip each of Pennsylvania, Florida and North Carolina, two trips to Wisconsin, and three trips to New York. Which resources will be completely used? A) only money B) only time C) time and money D) neither time nor money Answer: B Diff: 2 Page Ref: 68 Section Heading: Graphical Solutions of Linear Programming Models Keywords: slack variables AACSB: Analytical thinking Lame Example Furniture Company makes two products for its adoring public: chairs (C)and tables (T). Each chair requires 5 hours of labor (L) and 4 linear feet of rich mahogany (M), and each table requires 3 hours of labor and 20 linear feet of rich mahogany. The company has 240 labor hours available this week, and the warehouse has 700 linear feet of rich mahogany available. Profit for each chair is $300 and for each table is $1500. 103) If the furniture company produces twenty tables and thirty-six chairs, which of the two resources will be completely used? A) labor only B) rich mahogany only C) both labor and rich mahogany D) neither labor and rich mahogany Answer: A Diff: 2 Page Ref: 61 Section Heading: Graphical Solutions of Linear Programming Models Keywords: slack variables AACSB: Analytical thinking 25 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 104) Consider the following linear program: MAX z = 5x + 3y s.t. x - y ≤ 6 x≤1 The optimal solution: A) is infeasible. B) occurs where x = 1 and y = 0. C) occurs where x = 0 and y = 1. D) results in an objective function value of 5. Answer: D Diff: 2 Page Ref: 62 Section Heading: Graphical Solutions of Linear Programming Models Keywords: slack variables AACSB: Analytical thinking 105) The first step in solving a graphical linear programming model is to: A) plot the model constraints as equations on the graph and indicate the feasible solution area. B) plot the objective function and move this line out from the origin to locate the optimal solution point. C) solve simultaneous equations at each corner point to find the solution values at each point. D) determine which constraints are binding. Answer: A Diff: 1 Page Ref: 59 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphic solution, steps for solving a graphical linear prog model AACSB: Analytical thinking 106) The optimal solution of a minimization problem is at the extreme point ________ the origin. A) farthest from B) closest to C) exactly at D) parallel to Answer: B Diff: 2 Page Ref: 73 Section Heading: A Minimization Model Example Keywords: minimization problem AACSB: Analytical thinking 26 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 107) Multiple optimal solutions provide ________ flexibility to the decision maker. A) greater B) less C) greater or equal D) less or equal Answer: A Diff: 2 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: irregular types of linear programming problems AACSB: Analytical thinking 108) Which of the following special cases does not require reformulation of the problem in order to obtain a solution? A) unboundedness B) infeasibility C) alternate optimality D) Each one of these cases requires reformulation. Answer: C Diff: 3 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: irregular types of linear programming problems AACSB: Analytical thinking 109) If the feasible region for a linear programming problem is unbounded, then the solution to the corresponding linear programming problem is ________ unbounded. A) always B) sometimes C) never D) There is not enough information to complete this statement. Answer: B Diff: 3 Page Ref: 78 Section Heading: Irregular Types of Linear Programming Problems Keywords: irregular types of linear programming problems, unboundedness AACSB: Analytical thinking 27 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 110) Solve the following graphically: Max z = 3x1 + 4x2 s.t. x1 + 2x2 ≤ 16 2x1 + 3x2 ≤ 18 x1 ≥ 2 x2 ≤ 10 x1, x2 ≥ 0 What are the optimal values of x1, x2, and z? Answer: x1 = 9, x2 = 0, z = 27 Diff: 3 Page Ref: 59 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, simultaneous solution AACSB: Analytical thinking 28 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 111) A novice business analyst develops the following model to determine the optimal combination of socks and underwear to take on his next business trip. The model is as follows: Maximize 5S + 7U subject to: 3S - 2U ≤ 45 7S + 3U ≤ 33 2S + 8U ≤ 70 Solve this problem graphically and determine how many of each item the analyst should pack. Answer: The optimal solution lies at the point representing 1.08 socks and 8.48 underwear. I suppose this is why I referred to the analyst as a novice. Corner points and the objective function value in (Socks,Underwear) order are: Z(0,0) = 0 Z(4.714,0) = 23.57 Z(0,8.75) = 61.25 Z(1.08. 8.48) = 64.76 optimal Diff: 3 Page Ref: 59 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution AACSB: Analytical thinking 29 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 112) Nathan enters the final exam period needing to pull off a miracle to pass his three toughest classes, Healthy Life Choices, Success Central, and Walking Fitness. Naturally he would also prefer to expend as little effort as possible doing so and as luck would have it, he knows a guy that can help optimize his time and GPA using the magic of management science. The model they develop is built around the notion of time spent studying and doing all the assignments he has neglected throughout the semester. The model is as follows, where S represents time spent studying (in minutes) and A represents time spent making up assignments (also in minutes). Maximize Z = 6S + 4A subject to: HLC 12S + 10A ≥ 100 SC 6S + 8A ≥ 64 W 7S - 3A ≥ 36 Graphing was never one of Nathan's strengths, so it is up to you to develop a graphical solution to his problem and advise him on how much time should be invested in studying and how much time should be spent catching up on assignments. Answer: The two corner points meriting investigation are (in (Studying, Assignments) order) Z(10.67,0) = 64 Z(6.48,3.13) = 51.46 the optimal solution So, 6 minutes of studying and 3 minutes of working on assignments was all that was required for my first born to successfully complete his first semester with something other than a 0.0 GPA. Sad, but true. Diff: 2 Page Ref: 73 Section Heading: A Minimization Model Example Keywords: graphical solution AACSB: Analytical thinking 30 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 113) Consider the following linear program: MAX Z = 25A + 30B s.t. 12A + 15B ≤ 300 8A + 7B ≤ 168 10A + 14B ≤ 280 Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z. Answer: Solution shown below. A = 11.67, B = 10.67 Diff: 2 Page Ref: 59 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical linear programming AACSB: Analytical thinking 31 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 114) Consider the following linear program: MIN Z = 50A + 60B s.t. 6A + 8B ≤ 300 14A + 7B ≥ 196 A ≥ 10 B≥8 Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z. Answer: A = 10, B = 8, Z = 980 Diff: 2 Page Ref: 59 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical linear programming AACSB: Analytical thinking 32 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 115) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. If this is a maximization, which extreme point is the optimal solution? Answer: E Diff: 1 Page Ref: 64 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, extreme points, feasible region AACSB: Analytical thinking 33 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 116) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. What are the equations for any two greater than or equal constraints for this problem? Answer: The three greater than or equal constraints are A≥10, B≥8, 14A+7B≥98 Diff: 3 Page Ref: 64 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, extreme points, feasible region AACSB: Analytical thinking 34 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 117) A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. Provide a full description of the type of constraint is represented by line JK. Answer: Line JK is a nonbinding, greater than or equal constraint. It cannot be a less than or equal constraint because then the problem would be infeasible. Diff: 2 Page Ref: 77 Section Heading: Irregular Types of Linear Programming Problems Keywords: graphical solution, multiple optimal solutions AACSB: Analytical thinking 118) Consider the following linear programming problem: Max Z = $15x + $20y Subject to: 8x + 5y ≤ 40 0.4x + y ≥ 4 x, y ≥ 0 Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first constraint? Answer: x = 0, y = 8, revenue = $160, s1= 0 Diff: 2 Page Ref: 68 Section Heading: Graphical Solutions of Linear Programming Models Keywords: graphical solution, slack variables AACSB: Analytical thinking 35 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 119) Given this model Maximize Z = 6S + 4A subject to: 12S + 10A ≥ 100 6S + 8A ≥ 64 7S - 3A ≥ 36 What is the optimal solution and the surplus associated with the first constraint? Answer: The optimal solution lies at S = 6.48 and A = 3.13. The s1 variable is 9.1892 Diff: 2 Page Ref: 74 Section Heading: A Minimization Model Example Keywords: surplus AACSB: Analytical thinking 120) The poultry farmer decided to make his own chicken scratch by combining alfalfa and corn in rail car quantities. A rail car of corn costs $400 and a rail car of alfalfa costs $200. The farmer's chickens have a minimum daily requirement of vitamin K (500 milligrams) and iron (400 milligrams), but it doesn't matter whether those elements come from corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams of vitamin K and 50 milligrams of iron. Formulate the linear programming model for this situation. Answer: Min Z = $4005C + $200A Subject to: 150C + 250A ≥ 500 75C + 50A ≥ 400 C, A ≥ 0 Diff: 3 Page Ref: 56 Section Heading: A Maximization Model Example Keywords: constraint, model formulation AACSB: Analytical thinking 121) Consider the following linear programming problem: MIN Z = 3x1 + 2x2 Subject to: 2x1 + 3x2 ≥ 12 5x1 + 8x2 ≥ 37 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution? Answer: 9.25 at x1 = 0 and x2 = 4.625 Diff: 3 Page Ref: 64 Section Heading: Graphical Solutions of Linear Programming Models Keywords: minimization problem AACSB: Analytical thinking 36 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 122) Consider the following linear programming problem: MIN Z = 3x1 + 2x2 Subject to: 2x1 + 3x2 ≥ 12 5x1 + 8x2 ≥ 37 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution? Answer: 9.25 at x1 = 0 and x2 = 4.625 Diff: 3 Page Ref: 64 Section Heading: Graphical Solutions of Linear Programming Models Keywords: minimization problem AACSB: Analytical thinking 123) Ponder the following linear programming problem: MIN Z = 3x1 + 8x2 Subject to: 3x1 + 4x2 ≥ 52 3x1 + 4x2 ≥ 38 x1, x2 ≥ 0 What is minimum cost and the value of x1 and x2 at the optimal solution? Answer: 52 at x1 = 17.33 and x2 = 0.0 Diff: 3 Page Ref: 64 Section Heading: Graphical Solutions of Linear Programming Models Keywords: minimization problem AACSB: Analytical thinking 124) The international man of mystery knew the finest haberdashers the world over and constantly sought to expand his dazzling array of fine suits, ties, and cufflinks. Closet space was at a premium however, so purchases were carefully weighed. Each suit provides 23 units of dazzlement, each tie 14, and a set of cufflinks is worth an easy 8. A suit takes up 0.5 cubic feet of closet space and $900 of budget. A tie costs $135 and cufflinks cost $100 per set. Cufflinks are tiny – even in the original box, they take up only .01 cubic feet while ties occupy a lusty .25 cubic feet. He has budgeted $12,000 for clothes on this trip and has 20 cubic feet of closet space left to fill. Formulate an objective function and constraints to model this situation. Answer: Max Dazzlement = 23S + 14T + 8C subject to: 900S + 135T + 100C ≤ 12,000 0.5S + 0.25T + 0.01C ≤ 20 Diff: 3 Page Ref: 56 Section Heading: A Maximization Model Example Keywords: linear programming formulation AACSB: Analytical thinking 37 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 125) Ponder the following linear programming problem: Max Z = 5x1 + 6x2 Subject to: 3x1 + 4x2 ≤ 76 8x1 + 9x2 ≤ 123 3x1 + 3x2 ≤ 56 x1, x2 ≥ 0 What is the optimal solution point? Answer: 12.31 at x1 and 2.72 at x2 for an objective function value of 77.897 Diff: 3 Page Ref: 62 Section Heading: A Maximization Model Example Keywords: optimal solutions AACSB: Analytical thinking 126) List the four properties of linear programming models and provide an example of a violation of each. Answer: Properties and brief discussions are contained in the table. Counter examples will vary. Proportionality Additivity Divisibility Certainty The slope of a constraint or objective function is constant. There are no increasing or decreasing marginal returns on either. Strictly linear functions - there are no interaction effects among decision variables. Non-integer values of decision variables are OK. All model parameters are known exactly. Diff: 2 Page Ref: 79 Section Heading: Characteristics of Linear Programming Problems Keywords: linear programming properties AACSB: Application of knowledge 127) Formulate all elements of linear program to model your university effort. Include a narrative that explains each of the components. Answer: Answers will vary, perhaps dramatically. A noble objective function would seek to maximize a GPA or minimize total cost. Constraints would likely include budget, hours in a day, financial capital, conflicts with social endeavors, and others. Diff: 2 Page Ref: 54 Section Heading: Model Formulation Keywords: linear programming properties AACSB: Application of knowledge 38 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 128) Consider the following linear programming problem: MIN Z = 10x1 + 20x2 Subject to: x1 + x2 ≥ 12 2x1 + 5x2 ≥ 40 x2 ≤ 13 x1, x2 ≥ 0 At the optimal solution, what is the value of surplus associated with constraint 1 and constraint 3, respectively? Answer: constraint 1: (0 surplus), constraint 2: (7.667 surplus) Diff: 2 Page Ref: 72 Section Heading: A Minimization Model Example Keywords: graphical solution AACSB: Analytical thinking 129) Given this set of constraints, for what objective function is the point x = 5, y = 3 in the feasible region? s.t 3x + 6y ≤ 30 10x + 10y ≤ 60 10x + 15y ≤ 90 Answer: No objective function can move that point into the feasible region. Diff: 2 Page Ref: 62 Section Heading: Graphical Solutions of Linear Programming Models Keywords: feasibility, constraints AACSB: Analytical thinking 130) Consider the following linear programming problem: MIN Z = 2x1 + 3x2 Subject to: x1 + 2x2 ≤ 20 5x1 + x2 ≤ 40 4x1 + 6x2 ≤ 60 x1, x2 ≥ 0 What is the optimal solution? Answer: Multiple optimal solutions exist between the extreme point (0,10) and (6.92,5.38) along the line with a slope of -2/3. Diff: 2 Page Ref: 72 Section Heading: A Minimization Model Example Keywords: graphical solution, multiple optimal solutions AACSB: Analytical thinking 39 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 131) A company producing a standard line and a deluxe line of fidget spinners has the following time requirements (in minutes) in departments where either model can be processed. Stamping Extruding Fidget Testing Standard 0.3 0.25 1 Deluxe 0.4 0.5 1.5 The standard models contribute $2 each and the deluxe $3 each to profits. Because the company produces other items that share resources used to make the fidget spinners, the stamping machine is available only 15 minutes per hour, on average. The extruding unit has 20 minutes available each hour. There are two ADHD certified inspectors for fidget testing, but their availability is only 45 minutes per hour because they're easily distracted. Let S = number of standard fidget spinners produced per hour D = number of deluxe fidget spinners produced per hour Write the formulation for this linear program and solve it using the graphical method. 40 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Answer: Max $2S + $3D s.t 0.3S + 0.4D ≤ 15 0.25S + 0.5D ≤ 20 1S + 1.5D ≤ 45 The optimal product mix is to make 30 Deluxe units and no Standard units. Diff: 3 Page Ref: 56 Section Heading: A Maximization Model Example Keywords: formulation, objective function, constraints AACSB: Analytical thinking 41 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Introduction to Management Science, 13e, Global Edition (Taylor) Chapter 3 Linear Programming: Computer Solution and Sensitivity Analysis 1) The shadow price for a positive decision variable is 0. Answer: TRUE Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: shadow price, sensitivity analysis AACSB: Analytical thinking 2) When the right-hand sides of two constraints are both increased by one unit, the value of the objective function will be adjusted by the sum of the constraints' prices. Answer: FALSE Diff: 3 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitive analysis, right-hand-side AACSB: Analytical thinking 3) Most computer linear programming packages readily accept constraints entered in fractional form, such as X1/X3. Answer: FALSE Diff: 1 Page Ref: 100 Section Heading: Computer Solution Keywords: computer solution, formulation, constraint AACSB: Analytical thinking 4) Sensitivity ranges can be computed only for the right-hand sides of constraints. Answer: FALSE Diff: 1 Page Ref: 105 Section Heading: Sensitivity Analysis Keywords: computer solution AACSB: Analytical thinking 5) The marginal value of any scarce resource is the dollar amount one should be willing to pay for one additional unit of that scarce resource. Answer: TRUE Diff: 1 Page Ref: 102 Section Heading: Computer Solution Keywords: marginal value AACSB: Analytical thinking 6) Sensitivity analysis determines how a change in a parameter affects the optimal solution. Answer: TRUE Diff: 2 Page Ref: 104 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 1 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 7) The sensitivity range for an objective function coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal. Answer: TRUE Diff: 2 Page Ref: 105 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficient AACSB: Analytical thinking 8) The sensitivity range for an objective function coefficient is the range of values over which the profit does not change. Answer: FALSE Diff: 2 Page Ref: 105 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficient AACSB: Analytical thinking 9) The sensitivity range for a constraint quantity value is the range over which the shadow price is valid. Answer: TRUE Diff: 2 Page Ref: 107 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficient AACSB: Analytical thinking 10) If we change the constraint quantity to a value outside the sensitivity range for that constraint quantity, the shadow price will change. Answer: TRUE Diff: 2 Page Ref: 109 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, shadow price AACSB: Analytical thinking 11) The sensitivity range for a constraint quantity value is the range over which the optimal values of the decision variables do not change. Answer: FALSE Diff: 2 Page Ref: 109 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficient AACSB: Analytical thinking 12) Sensitivity analysis allows the modeler to relax the certainty assumption. Answer: TRUE Diff: 2 Page Ref: 105 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, parameter changes AACSB: Application of knowledge 2 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 13) The terms "shadow price" and "dual price" mean the same thing. Answer: TRUE Diff: 1 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 14) Sensitivity analysis can be used to determine the effect on the solution for changing several parameters at once. Answer: FALSE Diff: 2 Page Ref: 113 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 15) For a profit maximization problem, if the allowable increase for a coefficient in the objective function is infinite, then profits are unbounded. Answer: FALSE Diff: 2 Page Ref: 109 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 16) One type of sensitivity analysis is to add a new constraint to the model. Answer: TRUE Diff: 2 Page Ref: 113 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 17) To determine the change in the objective function for any increase in right-hand side, simply multiple the shadow price by the increase in the right-hand side. Answer: FALSE Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 18) The Allowable Increase for Calimari in the sensitivity report was 25 with a final value of 13, a shadow price of $16, and an objective coefficient of 10. Luigi added 5 units of Calimari and increased his profit by $80. Answer: TRUE Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 3 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 19) The reduced cost (shadow price) for a positive decision variable is ________. Answer: zero Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, shadow price AACSB: Analytical thinking 20) ________ is the analysis of the effect of parameter changes on the optimal solution. Answer: Sensitivity analysis Diff: 2 Page Ref: 104 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 21) The sensitivity range for a constraint quantity value is also the range over which the ________ is valid. Answer: shadow price Diff: 2 Page Ref: 105 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, shadow price AACSB: Analytical thinking 22) The sensitivity range for a(n) ________ coefficient is the range of values over which the current optimal solution point (product mix) will remain optimal. Answer: objective function Diff: 1 Page Ref: 105 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficient AACSB: Analytical thinking 4 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Table 3.1: Regular & Super Consider the following linear program, which maximizes profit for two products--regular (R) and super (S): MAX 50R + 75S s.t. 1.2 R + 1.6 S ≤ 600 assembly (hours) 0.8 R + 0.5 S ≤ 300 paint (hours) .16 R + 0.4 S ≤ 100 inspection (hours) Sensitivity Report: Cell $B$7 $C$7 Name Regular = Super = Final Value 291.67 133.33 Reduced Cost 0.00 0.00 Objective Coefficient 50 75 Allowable Increase 70 50 Allowable Decrease 20 43.75 Cell $E$3 $E$4 $E$5 Name Assembly (hr/unit) Paint (hr/unit) Inspect (hr/unit) Final Value 563.33 300.00 100.00 Shadow Price 0.00 33.33 145.83 Constraint R.H. Side 600 300 100 Allowable Increase 1E+30 39.29 12.94 Allowable Decrease 36.67 175 40 23) The optimal number of regular products to produce is ________, and the optimal number of super products to produce is ________, for total profits of ________. Answer: 291.67, 133.33, $24,583 Diff: 1 Page Ref: 100 Section Heading: Computer Solution Keywords: computer solution AACSB: Analytical thinking 24) If the company wanted to increase the available hours for one of their constraints (assembly, painting, or inspection) by two hours, they should increase ________. Answer: inspection Diff: 2 Page Ref: 107 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 25) The profit on the super product could increase by ________ without affecting the product mix. Answer: $50 Diff: 1 Page Ref: 109 Section Heading: Sensitivity Analysis Keywords: computer solution AACSB: Analytical thinking 5 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 26) If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by ________. Answer: $1,333 Diff: 2 Page Ref: 109 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 27) A change in the market has increased the profit on the super product by $5. Total profit will increase by ________. Answer: $667 Diff: 2 Page Ref: 107 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 6 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Table 3.2: Taco Loco Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. Max R = 14Z + 13Y + 17X subject to: Beef 2Z + 3Y + 4X ≤ 28 Cheese 9Z + 8Y + 11X ≤ 80 Beans 4Z + 4Y + 2X ≤ 68 X,Y,Z ≥ 0 The sensitivity report from the computer model reads as follows: 28) Taco Loco should try to purchase additional ________, but should not buy more ________. Answer: beef and cheese, beans Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: shadow price, sensitivity analysis AACSB: Analytical thinking 29) Taco Loco should produce both ________ but should not make any ________. Answer: Z and Y, X Diff: 1 Page Ref: 100 Section Heading: Computer Solution Keywords: computer solution, spreadsheets AACSB: Analytical thinking 7 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 30) Taco Loco will make the same quantity of X, Y, and Z if the amount of cheese at their disposal is between ________ pounds and ________ pounds. Answer: 74.67, 126 Diff: 2 Page Ref: 110 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking 31) For humanitarian reasons, Taco Loco decides they would rather make product X than product Y. The dollar amount that they can both increase the price of Y and reduce the price of X by to accomplish this reversal of demand is ________. Answer: 82 cents (81.8 cents) Diff: 2 Page Ref: 103 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, parameter changes AACSB: Analytical thinking 32) If Taco Loco reduces the price of the X product by about 82 cents, then their optimal product mix will contain ________ X. Answer: 0 units (none) Diff: 1 Page Ref: 113 Section Heading: Sensitivity Analysis Keywords: reduced cost AACSB: Analytical thinking 33) The amount in euros that a Parisian manager would be willing to pay is the ________ . Answer: marginal value Diff: 1 Page Ref: 104 Section Heading: Computer Solution Keywords: marginal value AACSB: Analytical thinking 34) The Allowable Increase in an Excel sensitivity report is found under the heading of ________ in the QM for Windows report. Answer: upper bound Diff: 1 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: upper bound, allowable increase, QM AACSB: Analytical thinking 35) The Shadow Price in an Excel sensitivity report is found under the heading of ________ in the QM for Windows report. Answer: dual value Diff: 1 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: dual value, shadow price, QM AACSB: Analytical thinking 8 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 36) For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs. and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: A) same product mix, different total profit. B) different product mix, same total profit as before. C) same product mix, same total profit. D) different product mix, different total profit. Answer: A Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 37) A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes., and the range of feasibility is from 130 minutes to 300 minutes, providing two additional machine hours will result in: A) the same product mix, different total profit. B) a different product mix, same total profit as before. C) the same product mix, same total profit. D) a different product mix, different total profit. Answer: D Diff: 3 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking Table 3.3 Beer, Etc. The production manager for Beer Etc. produces two kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. The manager can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week, respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. 38) If the production manager decides to produce of 400 bottles of light beer and 0 bottles of dark beer, it will result in slack of: A) malt only. B) wheat only. C) both malt and wheat. D) neither malt nor wheat. Answer: B Diff: 2 Page Ref: 108 Section Heading: Sensitivity Analysis and Graphical Solution Keywords: graphical solution, constraints AACSB: Analytical thinking 9 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 39) Which of the following is not a feasible solution for the scenario in Table 3.3? A) 0 L and 0 D B) 0 L and 400 D C) 200 L and 300 D D) 300 L and 200 D Answer: D Diff: 3 Page Ref: 108 Section Heading: Sensitivity Analysis Keywords: computer solution, infeasibility AACSB: Analytical thinking 40) What is the optimal weekly profit for the scenario in Table 3.3? A) $1000 B) $900 C) $800 D) $700 Answer: C Diff: 2 Page Ref: 99 Section Heading: Computer Solution Keywords: computer solution AACSB: Analytical thinking 41) Which of the following could not be a linear programming problem constraint? A) A + B ≤ -3 B) A - B ≤ -3 C) A - B ≤ 3 D) -A + B ≤ -3 Answer: A Diff: 2 Page Ref: 100 Section Heading: Computer Solution Keywords: graphical solution, feasibility AACSB: Analytical thinking 42) Use the constraints given below and determine which of the following points is feasible. 14x + 6y ≤ 42 x-y≤3 A) x = 1; y = 4 B) x = 2; y = 8 C) x = 2; y = 4 D) x = 3; y = 0.5 Answer: A Diff: 2 Page Ref: 100 Section Heading: Sensitivity Analysis Keywords: constraints AACSB: Analytical thinking 10 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 43) For the constraints given below, which point is in the feasible region of this minimization problem? 14x + 6y ≤ 42 x + 3y ≥ 6 A) x = 2; y = 5 B) x = 1; y = 2 C) x = 2; y = 1 D) x = 2; y = 3 Answer: B Diff: 2 Page Ref: 100 Section Heading: Sensitivity Analysis Keywords: constraints AACSB: Analytical thinking 44) What combination of x and y is a feasible solution that minimizes the value of the objective function? Min Z = 3x + 15y 2x + 4y ≥ 12 5x + 2y ≥ 10 A) x = 0; y = 3 B) x = 0; y = 5 C) x = 5; y = 0 D) x = 6; y = 0 Answer: C Diff: 3 Page Ref: 102 Section Heading: Computer Solution Keywords: feasibility, constraints AACSB: Analytical thinking 45) A shadow price reflects which of the following in a maximization problem? A) the marginal gain in the objective that would be realized by adding one unit of a resource B) the marginal gain in the objective that would be realized by subtracting one unit of a resource C) the marginal cost of adding additional resources D) the marginal gain of selling one more unit Answer: A Diff: 3 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: shadow price, sensitivity analysis AACSB: Analytical thinking 11 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 46) Given the following linear programming problem: Max Z = 15x + 20y s.t. 8x + 5y ≤ 40 4x + y ≥ 4 What would be the values of x and y that will maximize revenue? A) x = 5; y = 0 B) x = 0; y = 8 C) x = 0; y = 1 D) x = 1; y = 0 Answer: B Diff: 2 Page Ref: 102 Section Heading: Computer Solution Keywords: formulation, solution AACSB: Analytical thinking 47) Given the following linear program that maximizes revenue: Max Z = 15x + 20y s.t. 8x + 5y ≤ 40 4x + y ≥ 4 What is the maximum revenue at the optimal solution? A) $120 B) $160 C) $185 D) $200 Answer: B Diff: 2 Page Ref: 100 Section Heading: Computer Solution of a Transportation Problem Keywords: formulation, solution AACSB: Analytical thinking 48) For a maximization problem, the shadow price measures the ________ in the value of the optimal solution, per unit increase for a given ________. A) decrease, resource B) increase, parameter C) improvement, resource D) decrease, parameter Answer: C Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 12 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 49) Sensitivity analysis is the analysis of the effect of ________ changes on the ________. A) price, company B) cost, production C) parameter, optimal solution D) constraint, parameter Answer: C Diff: 1 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 50) For a linear programming problem, assume that a given resource has not been fully used. We can conclude that the shadow price associated with that constraint: A) will have a positive value. B) will have a negative value. C) will have a value of zero. D) could have a positive, negative or a value of zero. (no sign restrictions). Answer: C Diff: 3 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, shadow price AACSB: Analytical thinking 51) For a resource constraint, either its slack value must be ________ or its shadow price must be ________. A) negative, negative B) negative, zero C) zero, zero D) zero, negative Answer: C Diff: 1 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, shadow price AACSB: Analytical thinking 13 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Table 3.4: I am Ulysses Uncle Ulysses operates a small business: he produces three types of houses to sell to people wanting to get back to nature. Based on your discussion with your uncle you construct the following table based on your understanding of his weekly availability of labor. Item Birdhouse Doghouse Outhouse Capacity Profit/Unit Fabrication Assembly $15 1 2.5 $35 1.25 1.5 $58 1.75 4 30 hours 50 hours Painting 1 0.5 2 20 hours Crating 0.25 0.5 0.75 20 hours Based on the information in the table, you formulate the problem as a linear program. The labor needed for fabrication, assembly, painting, and crating is all dedicated solely to each function, i.e., none of the workers have been cross-trained. The Excel solution and the answer and sensitivity report are shown below. The Answer Report: 14 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 The Sensitivity Report: 52) Which additional resources would you recommend that Uncle Ulysses try to obtain? A) fabrication B) assembly C) paint D) crate Answer: A Diff: 1 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 53) Suppose Uncle Ulysses is required by contract with the American Birding Association to make one birdhouse each week. How would this affect his profits? A) Profits would increase by $15. B) Profits would decrease by $17.15. C) Profits would increase by $0.00. D) Profits would decrease by $1E + 30. Answer: B Diff: 3 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 15 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 54) Uncle Ulysses feels that his prices are too low, particularly for his birdhouses. How much would he have to charge for his birdhouses before it is profitable for him to make and sell them? A) $15.00 B) $17.15 C) $32.15 D) $47.15 Answer: C Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 55) Uncle Ulysses' available hours for crating have fallen from 20 hours to 15 hours because of a new "one-hour nap time" rule for this five-year-old worker. How will this affect his profits? A) Profits will increase by $7.69. B) Profits will decrease by $7.69. C) Profits will decrease by $12.31. D) Profits will not change. Answer: D Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 56) Uncle Ulysses can obtain an additional 10 hours of painting capacity free of charge by training his helper monkey to paint. If he did this, how would his profits be affected? A) Profit would increase by $6.92. B) Profits would decrease by $20. C) Profits would increase by $1.58. D) Cannot tell from the information provided. Answer: D Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 16 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 57) Uncle Ulysses is planning for next spring, and he is considering making only two products. Based on the results from the linear program, which two products would you recommend that he make? A) birdhouses and doghouses B) birdhouses and outhouses C) doghouses and outhouses D) He should continue to make all three. Answer: B Diff: 2 Page Ref: 114 Section Heading: Computer Solution Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 17 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Table 3.5: William Works William Works sells 3 types of T-shirts: Astro, Bling, and Curious. Manufacturing Astros requires 2 minutes of machine time and 30 minutes of tie-dying labor, and costs $18 in materials. Brand Bling requires 2.5 minutes of machine time and 35 minutes of labor, and costs $14 in materials to produce. Brand Curious requires 3 minutes of machine time and 40 minutes of labor, but costs only $10 to produce. There are 350 machining minutes available per week, 4750 tiedying labor minutes, and he has a budget of $3000. Brand Astro sells for $20, Brand Bling for $24, and Brand Curious for $30. The solution from QM for Windows is shown below. The ranging report from QM for Windows is shown below. 58) If William could acquire more of any resource, which would it be? A) adding resources cannot improve his profit B) money C) tie-dying labor D) machining time Answer: D Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, quantity ranges for constraints AACSB: Analytical thinking 18 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 59) If one of William's machines breaks down, it usually results in about 15 minutes of downtime. When this happens, Billy's profits are reduced by: A) $250. B) $180. C) $150. D) $350. Answer: C Diff: 2 Page Ref: 112 Section Heading: Linear Programming Models Keywords: sensitivity analysis, quantity ranges for constraints AACSB: Analytical thinking 60) William's accountant made an error, and the budget has been reduced from $3000 to $2500. William's profit will go down by: A) $0. B) $1167. C) $350. D) $4667. Answer: A Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking 61) William has decided that he can raise the price on the Curious t-shirt by 10% without losing sales. If he raises the price, his profits will: A) increase by $3. B) increase by $350. C) increase by $11.67. D) increase by $33. Answer: B Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking 19 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Table 3.6 Taco Loco Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. Max R = 14Z + 13Y + 17X subject to: Beef 2Z + 3Y + 4X ≤ 28 Cheese 9Z + 8Y + 11X ≤ 80 Beans 4Z + 4Y + 2X ≤ 68 X,Y,Z ≥ 0 The sensitivity report from the computer model reads as follows: 62) The local cheese vendor offers to sell Taco Loco 200 pounds of cheese for these three products. Taco Loco should: A) refuse to buy any cheese. B) buy less than 80 pounds of cheese for $1.45 per pound. C) buy 46 pounds or less of cheese for $1.45 or less. D) buy at least 126 pounds of cheese for $5.33 or less. Answer: C Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: shadow price, computer solution AACSB: Analytical thinking 20 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 63) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. Answer: C Diff: 2 Page Ref: 102 Section Heading: Computer Solution Keywords: computer solution, spreadsheets AACSB: Analytical thinking 64) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 pounds Answer: C Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking 65) How many pounds of beans will Taco Loco have left over if they produce the optimal quantity of products X, Y, and Z? A) 28.73 B) 39.27 C) 0 D) 1E + 30 Answer: A Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking 66) What is the increase in revenue if Taco Loco purchases 20 pounds of cheese for $1 and uses it optimally? A) $0 B) $9.09 C) $29.00 D) $158.18 Answer: C Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: shadow price, sensitivity analysis AACSB: Analytical thinking 21 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Table 3.7: The Love Boat Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. 67) What should Captain Stubing's objective function be? A) Max Z = 1500 Bar + 5000 Food + 17000 Excursion B) Max Z = Bar + Food + Excursion C) Max Z = 900 Bar + 1500 Food + 5000 Excursion D) Max Z = 5 Excursions + 12 Cuisine + 7 Bar + 150000 Budget Answer: A Diff: 2 Page Ref: 98 Section Heading: Sensitivity Analysis Keywords: objective function AACSB: Analytical thinking 68) What is the appropriate constraint for the budget? A) 1 Bar + 1 Food + 1 Excursion ≤ 150,000 B) 900 Bar + 1500 Food + 5,000 Excursion ≤ 150,000 C) 1,500 Bar + 5,000 Food + 17,000 Excursion ≤ 150,000 D) 7 Bar + 12 Food + 5 Excursion ≤ 150,000 Answer: B Diff: 2 Page Ref: 98 Section Heading: Sensitivity Analysis Keywords: constraints AACSB: Analytical thinking 22 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 69) What is the appropriate constraint for the requirement that there should be at least one different bar setup for every different type of food? A) Bar - Food ≤ 0 B) Bar + Food ≤ 0 C) Food - Bar ≤ 0 D) Food + Bar ≥ 0 Answer: C Diff: 2 Page Ref: 98 Section Heading: Sensitivity Analysis Keywords: constraints, formulation AACSB: Analytical thinking 70) Here's the sensitivity report for the decision variables. Which of these conclusions is correct? Cell $B$2 $C$2 $D$2 Name Bar Cuisine Excursion Final Value 12 12 24.24 Reduce Cost 0 0 0 Objective Coefficient 1500 5000 17000 Allowable Increase 1560 1660 1E+30 Allowable Decrease 1E+30 1E+30 3458.33333 A) If the cost of the Bar variable is reduced by more than 0, then more of it will be used. B) If the cost of the Bar variable is increased by more than 0, then more of it will be used. C) If the coefficient for the Cuisine variable rises to 1660, then more of it will be used. D) It doesn't matter how much money they make on excursions; the optimal answer will continue to be 24.24 of them. Answer: D Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficients AACSB: Analytical thinking 23 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 71) Here's a portion of the sensitivity analysis for the constraints. Which of these statements is best? Cell $E$10 $E$11 $E$6 $E$7 Name Bar/Food Budget Excursions Restaurant Final Value 0 150000 24.24 12 Shadow Price 1560 3.4 0 -1660 Constraint R.H. Side 0 150000 5 12 Allowable Increase 5 1E+30 19.24 16 Allowable Decrease 16 96200 1E+30 5 A) If the budget rises to $150,001, then the optimal mix will result in an increased revenue of $3.40. B) If the excursions rise to 6, then the optimal mix will result in increased revenue of $19.24. C) If the restaurant constraint increased to 13, the optimal mix will result in increased revenues of $1,660. D) If the bar/food constraint rises to 1560, then the revenue will rise by a factor of 16. Answer: A Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, quantity ranges for constraints AACSB: Analytical thinking 72) Based on the variable cells sensitivity report, what conclusion is best? Cell $B$2 $C$2 $D$2 Name Bar Cuisine Excursion Final Value 12 12 24.24 Reduced Cost 0 0 0 Objective Coefficient 1500 5000 17000 Allowable Increase 1560 1660 1E+30 Allowable Decrease 1E+30 1E+30 3458.33333 A) The value of Excursion can be infinite, since 1E + 30 is 10 to the 30th power. B) The values of Bar, Cuisine, and Excursion are all equal to zero. C) The values of Bar and Cuisine can be negative since they have allowable decreases of 1E + 30. D) The optimal value for the objective function is $490,080 Answer: D Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: objective function AACSB: Analytical thinking 24 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 73) Here's a lovely portion of the sensitivity report for the constraints. Which of these conclusions is reasonable? Cell $E$10 $E$11 $E$6 $E$7 $E$8 $E$9 Name Bar/Food Budget Excursions Restaurant Bar Low Bar High Final Value 0 150000 24.24 12 12 12 Shadow Price 1560 3.4 0 -1660 0 0 Constraint R.H. Side 0 150000 5 12 7 28 A) Captain Stubing is scheduling more Excursions than he should be. B) Captain Stubing should exhaust his Budget. C) There is no Bar or Food being used. D) The value for Restaurant will rise by $1,660 for each additional cuisine required. Answer: B Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: objective function AACSB: Analytical thinking 74) How should the requirement that the bar setups should change at least every other day but no more than twice per day? A) 1 Bar ≥ 7; 1 Bar ≤ 28 B) 7 ≤ 1 Bar ≤ 28 C) 1 Bar ≤ 28 D) 1 Bar ≥ 7 Answer: A Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: objective function AACSB: Analytical thinking 25 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 75) Using this snippet of the sensitivity report for variable cells, which of these conclusions is best? Cell $B$13 $C$13 $D$13 Name A B C Final Value 9 0 0 Reduced Cost 0 -2 -2 Objective Coefficient 5 6 1 Allowable Increase 1E+30 2 2 Allowable Decrease 1.25 1E+30 1E+30 A) Item A can drop in value all the way down to 1.25 before it harms the result. B) Items B and C are the only elements in the final model. C) The final value of this problem is 9. D) Insisting that one additional unit of B, be included in the model will reduce the profit by $2. Answer: D Diff: 1 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficients AACSB: Analytical thinking 76) Using this snippet of the sensitivity report for constraints, which of these conclusions is best? Cell $E$15 $E$16 $E$17 $E$18 Name One Two Three Four Final Value 45 54 27 72 Shadow Price 1 0 0 0 Constraint R.H. Side 45 56 67 78 Allowable Allowable Increase Decrease 1.666666667 45 1E+30 2 1E+30 40 1E+30 6 A) None of items Two, Three or Four is being used. B) Adding two units of One will increase the objective function value by two. C) Taking away four units of One will lower the objective function value by four. D) The most valuable resource is Four. Answer: C Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking 26 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Table 3.8: Tracksaws, Inc. Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table. Formulation: Let x = number of tractors produced per period y = number of lawn mowers produced per period MAX 30x + 30y subject to 2x + y ≤ 60 2x + 3y ≤ 120 x ≤ 45 The graphical solution is shown below. 27 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 77) How many tractors and saws should be produced to maximize profit, and how much profit will they make? Answer: 15 tractors and 30 saws for $1350 in profit Diff: 2 Page Ref: 100 Section Heading: Computer Solution Keywords: graphical solution, simultaneous solution AACSB: Analytical thinking 78) Determine the sensitivity range for the profit for tractors. Answer: 20 ≤ x ≤ 60 Diff: 2 Page Ref: 110 Section Heading: Sensitivity Analysis Keywords: graphical solution, sensitivity analysis AACSB: Analytical thinking 79) What is the shadow price for assembly? Answer: 0 Diff: 1 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: graphical solution, sensitivity analysis AACSB: Analytical thinking 80) What is the shadow price for fabrication? Answer: $7.50 Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking 81) What is the maximum amount a manager would be willing to pay for one additional hour of machining time? Answer: $1357.50 - $1350 = $7.50 Diff: 3 Page Ref: 114 Section Heading: Sensitivity Analysis and Graphical Solution Keywords: graphical solution, sensitivity analysis AACSB: Analytical thinking 82) A breakdown in fabrication causes the available hours to drop from 120 to 90 hours. How will this impact the optimal number of tractors and mowers produced? Answer: x = 22.5, y = 15, Z = 1125, so profits will fall by $1350 - $1125 = $225. Students may also answer the question by determining the sensitivity range, which is from 60 to 180 hours, resulting in a profit change of 30 × $7.5 = $225. Diff: 3 Page Ref: 108 Section Heading: Sensitivity Analysis and Graphical Solution Keywords: graphical solution, sensitivity analysis AACSB: Analytical thinking 28 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 83) What is the range for the shadow price for assembly? Answer: allowable decrease = 45 - 15 = 30, and allowable increase is ∞. Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis and Graphical Solution Keywords: graphical solution, sensitivity analysis AACSB: Analytical thinking Table 3.9: Zen Nail Spa Zen Nail Spa in Albuquerque stocks four colors of nail polish, pink (Pi), white (W), blue (B), and purple (Pu). Depending on the color requested, the client pays a different price due to drying times and need to touch up coverage. The pink color yields a profit of $100, white $150, blue $120, and purple $125. Bottles of pink nail polish take up one unit of shelf space and all other colors take up two units each. The total shelf space available in the storage cabinet and display is 108 units. Three of the colors (all except blue) require some mixing time. Pink takes three minutes, white takes five minutes, and purple takes a minute. The mixing technician can devote only two hours to these duties as she also runs the register at the Spa and the laser tag next door. Past demand has demonstrated that demand for pink and blue do not exceed 25 units each per week. However, the minimum weekly demand for white, blue and purple colors must be at least 50 units. The sensitivity report appears below: 84) How much space will be left unused? How many minutes of idle time remain for setting up the display? Answer: 0, 0 Diff: 3 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 29 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 85) Use the LP output to answer these two questions. (a) To what value can the per bottle profit on white nail polish drop before the solution (product mix) would change? (b) By how much can the per bottle profit on purple nail polish increase before the solution (product mix) would change? Answer: a) 145 b) 1 Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 86) Use the LP output to answer these two questions. (a) By how much can the amount of space decrease before there is a change in the profit? (b) What is the impact on profit if white, blue and purple stocking levels must equal at least 52 units? Answer: a) 0 b) drops by $82.50 Diff: 3 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 87) You are offered the chance to obtain more space. The offer is for 10 units and the total price is $1000. What should you do? Why? Answer: Reject the offer because the $100 per unit cost exceeds the shadow price of $80. Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: computer solution, sensitivity analysis AACSB: Analytical thinking 88) Max Z = 4x1 + 3x2 Subject to: 6x1 + 2x2 ≤ 24 15x1 + 20x2 ≤ 60 x1, x2 ≥ 0 Determine the sensitivity range for each constraint. Answer: constraint 1: 6 - 24 constraint 2: 60 - 240 Diff: 3 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, sensitivity range for right hand sides AACSB: Analytical thinking 30 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 89) Max Z = 5x1 + 3x2 Subject to: 6x1 + 2x2 ≤ 18 15x1 + 20x2 ≤ 60 x1, x2 ≥ 0 Determine the sensitivity range for each objective function coefficient. Answer: x1: 2.25 - 9.0, x2: 1.667 - 6.667 Diff: 3 Page Ref: 107 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis/range for objective function coefficients AACSB: Analytical thinking 90) Max Z = 3x1 + 3x2 Subject to: 10x1 + 4x2 ≤ 60 25x1 + 50x2 ≤ 200 x1, x2 ≥ 0 Determine the sensitivity range for each objective function coefficient. Answer: x1: 1.5 - 7.5, x2: 1.2 - 6.0 Diff: 3 Page Ref: 107 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis/range for objective function coefficients AACSB: Analytical thinking 31 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Table 3.10: The Love Boat Captain Stubing of The Pacific Princess seeks to maximize the return for their scheduled 14 day tour of Europe and has a number of options available to him. He can ply his guests with alcohol, upsell them on fancier restaurant fare or include more expensive excursion options. These alternatives are not without tradeoffs, since different guests prefer different options, depending largely on their age and wherewithal. Among the limitations Captain Stubing must consider is the number of excursions; they must offer at least five alternatives per day for each the ten days they will reach port. In addition, the restaurant choices must exceed 12 major styles of cuisine and the bar themes down in The Grotto should rotate every other day for the 14 days. It's possible to rotate them twice a day, but any more than that and poor Isaac spends more time tearing down and setting up than he does mixing libations. Ideally, there should be at least one different bar theme for every cuisine type. The total budget for excursions, restaurants and bar has been set by the parent company at $150,000. It costs $1,500 to stock supplies for a major cuisine category, it costs $5,000 to include each different excursion, and it costs $900 to set up with a different bar theme. Based on historical data, Captain Stubing believes that each new bar setup will generate $1,500 profit, each new cuisine type will bring in $5,000, and each excursion type will generate $17,000 for the ship. 91) What are the appropriate objective function and constraints for this scenario? Answer: Max Z = 1500B + 5000C + 17000E subject to: 900B + 1500C + 5000E ≤ 150,000 E≥5 C ≥ 12 B≥7 B ≤ 28 C-B≤0 Diff: 3 Page Ref: 104 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 32 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 92) Captain Stubing runs the LP model associated with the scenario and reads the following about the variable cells in the Excel sensitivity report. Provide an interpretation. Cell $B$2 $C$2 $D$2 Name Bar Food Excursion Final Value 12 12 24.24 Reduced Cost 0 0 0 Objective Coefficient 1500 5000 17000 Allowable Increase 1560 1660 1E+30 Allowable Decrease 1E+30 1E+30 3458.33333 Answer: There should be 12 different bar setups and cuisine types and 24.24 excursions. The Bar decision variable has an allowable increase of $1,560, so if the profit on a bar setup increased by that amount over the current value, i.e., all the way up to $3,060, the bar setups would remain the same at 12. The food types can increase by up to $1,660 per type, or up to $6,660 while remaining at 12 as the best number. Excursion profit can drop by up to $3,458 from the current value of $17,000 without changing from the recommended 24.24 value. The actual profit earned would of course change if these parameters stayed within their allowable increases and decreases, but the number of food, bar, and excursion types would remain at 12, 12 and 24 (and some change). Diff: 3 Page Ref: 111 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 93) Captain Stubing runs the LP model associated with the scenario and reads the following about the constraints in the Excel sensitivity report. Gopher is unable to provide an interpretation, but you volunteer to provide insight on the Restaurant and Excursions portion of the sensitivity report. Cell $E$10 $E$11 $E$6 $E$7 Name Bar/Food Budget Excursions Restaurant Final Value 0 150000 24.24 12 Shadow Price 1560 3.4 0 -1660 Constraint R.H. Side 0 150000 5 12 Allowable Increase 5 1E+30 19.24 16 Allowable Decrease 16 96200 1E+30 5 Answer: The Restaurant constraint has a shadow price of -$1,660 which means that for every one more cuisine variety required, the profit will drop by $1,660. If we required two more, profit would drop by $3320, and so on, up to requiring 16 additional meal types. Beyond that, the $1,660 cost would not be a correct estimate. For each type of cuisine dropped, from 12 to 11, the same figure hold, up to a reduction of five types of cuisine. Excursions has no shadow price — it is not a binding constraint, so we can actually reduce the number of excursions quite a bit, but 19.24 down to the required minimum of 5 per day. Diff: 2 Page Ref: 114 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 33 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 94) Using just the Constraints portion of the sensitivity report, indicate which of Captain Stubing's limitations are reducing his profit. Cell $E$10 $E$11 $E$6 $E$7 $E$8 $E$9 Name Bar/Food Budget Excursions Restaurant Bar Low Bar High Final Value 0 150000 24.24 12 12 12 Shadow Price 1560 3.4 0 -1660 0 0 Constraint R.H. Side 0 150000 5 12 7 28 Allowable Increase 5 1E+30 19.24 16 5 1E+30 Allowable Decrease 16 96200 1E+30 5 1E+30 16 Answer: Three of the constraints have shadow prices of zero, meaning they are non-binding and thus do not limit his profit. The Bar/Food combination, that is the requirement that there should be at least one bar type for each cuisine type, is holding him back. The budget constraint also limits the profit, for each additional budget dollar he had to start the cruise, he could generate an additional $3.40. If the right hand side of these constraints were increased, then additional profit could be earned. The restaurant constraint also limits profit, but since the shadow price is negative, an additional increase of the RHS reduces the profit. If the number of cuisine type drops by one, the an additional $1,660 can be made. Diff: 3 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 95) Captain Stubing eyes the sensitivity report for his decision variables and Julie McCoy, Cruise Director, studies it. Her sneeze obscures part of the printout, leaving the captain scratching his bald head about the values of each of the three variables, Bar, Food and Excursion. Does he need all three? How would he know simply by reading the remaining legible portion of the report? Cell $B$2 $C$2 $D$2 Name Bar Food Excursion Final Value 12 12 24.24 Reduced Cost 0 0 0 Objective Coefficient 1500 5000 17000 Allowable Increase 1560 1660 1E+30 Allowable Decrease 1E+30 1E+30 3458.33333 Answer: As luck would have it, we know that all three have positive values in the final solution. None of them shows as having a reduced cost, which means that they all must be in the solution. Diff: 2 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 34 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 96) Provide an interpretation of the Ranging Report from QM Answer: There should be 12 different bar setups and cuisine types and 24.24 excursions. The Bar decision variable has an upper bound of $3,060, so if the bar profit increases all the way up to $3,060, the bar setups would remain the same at 12. The food types can increase by up to $1,660 per type, or up to $6,660 while remaining at 12 as the best number. Excursion profit can drop by up to $3,458 from the current value of $17,000 without changing from the recommended 24.24 value. The actual profit earned would of course change if these parameters stayed within their allowable increases and decreases, but the number of food, bar, and excursion types would remain at 12, 12 and 24 (and some change). Diff: 3 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 97) Provide an interpretation of the Budget, Excursions constraints portion of the Ranging report for Captain Stubing. Answer: The Restaurant constraint has a dual value of -$1,660 which means that for every one more cuisine variety required, the profit will drop by $1,660. If we required two more, profit would drop by $3,320, and so on, up to requiring 16 additional meal types. Beyond that, the $1,660 cost would not be a correct estimate. For each type of cuisine dropped, from 12 to 11, the same figure hold, up to a reduction of five types of cuisine. Excursions has no dual value - it is not a binding constraint, so we can actually reduce the number of excursions quite a bit, but 19.24 down to the required minimum of 5 per day. Diff: 3 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis AACSB: Analytical thinking 35 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 98) Interpret this sensitivity report for the variable cells. Cell $B$13 $C$13 $D$13 Name A B C Final Value 9 0 0 Reduced Cost 0 -2 -2 Objective Coefficient 5 6 1 Allowable Increase 1E+30 2 2 Allowable Decrease 1.25 1E+30 1E+30 Answer: Decision variable A is the only variable that appears in the optimal answer. Nine units of A are optimal and the coefficient is 5, so the objective function value is 45. The optimal answer will remain nine units of A as long as the coefficient remains in the range of 3.75 to infinity. Decision variable B, with a coefficient of 6, is not used in the optimal answer. If the coefficient of B increased to 8 or beyond, it would enter the model with a positive value. If the value of B's coefficient drops by any amount, it will not enter the decision space. Similarly, C with an objective coefficient of 1, is not in the answer unless the coefficient increases to 3 or beyond. If we added a constraint that required either B or C to enter the solution, the value of the objective function would drop by 2, from 45 to 43. Diff: 3 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, objective coefficients AACSB: Analytical thinking 99) Interpret this sensitivity report for the constraints. Cell $E$15 $E$16 $E$17 $E$18 Name One Two Three Four Final Value 45 54 27 72 Shadow Price 1 0 0 0 Constraint R.H. Side 45 56 67 78 Allowable Increase 1.666666667 1E+30 1E+30 1E+30 Allowable Decrease 45 2 40 6 Answer: Constraint One is the only binding constraint; it has a shadow price of 1, meaning that if the RHS increased by 1, the optimal value of the objective function would rise by 1. This works in the very limited range up to 46.6666667. If the RHS dropped by 1, the objective function value would drop by 1 all the way down to a RHS equal to 0. The other constraints have slack; if constraint Two's RHS drops by 2 or more, the optimal answer would change. Constraint Four would become binding if the RHS was 72 or lower and constraint Three enters the picture if the RHS drops to 27 or lower. For the moment, any increase in the RHS for Two, Three or Four would have no impact on the optimal answer. Diff: 3 Page Ref: 112 Section Heading: Sensitivity Analysis Keywords: sensitivity analysis, quantity ranges for constraints AACSB: Analytical thinking 36 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Introduction to Management Science, 13e, Global Edition (Taylor) Chapter 4 Linear Programming: Modeling Examples 1) Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem. Answer: TRUE Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: formulation, product mix problem AACSB: Analytical thinking 2) Product mix problems cannot have greater-than-or-equal-to (≥) constraints. Answer: FALSE Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking 3) When using a linear programming model to solve the diet problem, the objective is generally to maximize profit. Answer: FALSE Diff: 2 Page Ref: 140-143 Section Heading: A Diet Example Keywords: objective function AACSB: Analytical thinking 4) When using a linear programming model to solve the diet problem, the objective is generally to maximize nutritional content. Answer: FALSE Diff: 2 Page Ref: 140-143 Section Heading: A Diet Example Keywords: objective function AACSB: Analytical thinking 5) Diet problems usually maximize nutritional value. Answer: FALSE Diff: 2 Page Ref: 140-143 Section Heading: A Diet Example Keywords: diet example AACSB: Application of knowledge 6) In most media selection decisions, the objective of the decision maker is to minimize cost. Answer: FALSE Diff: 2 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: marketing problem, media selection AACSB: Application of knowledge 1 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 7) In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the audience exposure. Answer: TRUE Diff: 2 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: marketing problem, media selection AACSB: Application of knowledge 8) A linear programming model of a media selection problem is used to determine the relative value of each advertising media. Answer: FALSE Diff: 3 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: marketing problem, media selection AACSB: Application of knowledge 9) In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities. Answer: TRUE Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Analytical thinking 10) The constraint x + y = z is written in standard form. Answer: FALSE Diff: 2 Page Ref: 144 Section Heading: An Investment Example Keywords: standard form AACSB: Application of knowledge 11) In an unbalanced transportation model, supply does not equal demand, and supply constraints must have ≤ signs. Answer: FALSE Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Analytical thinking 12) Transportation problems can have solution values that are non-integer and must be rounded. Answer: FALSE Diff: 3 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: transportation problem, solution AACSB: Analytical thinking 2 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 13) In a transportation problem, the supply constraint represents the maximum amount of product available for shipment or distribution at a given source (plant, warehouse, mill). Answer: TRUE Diff: 1 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Application of knowledge 14) In a transportation problem, a demand constraint for a specific destination represents the amount of product demanded by a given destination (customer, retail outlet, store). Answer: TRUE Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Application of knowledge 15) A conservative approach to a balanced transportation model would be to make all constraints less-than-or-equal-to constraints. Answer: FALSE Diff: 2 Page Ref: 153 Section Heading: A Transportation Example Keywords: balanced transportation model, transportation model formulation AACSB: Application of knowledge 16) In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤). Answer: FALSE Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Application of knowledge 17) Blending problems usually require algebraic manipulation in order to write the LP in "standard form." Answer: TRUE Diff: 1 Page Ref: 156-160 Section Heading: A Blend Example Keywords: blending AACSB: Application of knowledge 18) Fractional relationships among variables are considered standard form in a blending problem. Answer: FALSE Diff: 1 Page Ref: 156 Section Heading: A Blend Example Keywords: blending AACSB: Application of knowledge 3 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 19) Data envelopment analysis indicates which type of service unit makes the highest profit. Answer: FALSE Diff: 1 Page Ref: 165 Section Heading: A Data Envelopment Analysis Example Keywords: blending AACSB: Analytical thinking 20) In a classic blending problem, revenue is maximized by subtracting cost from profit. Answer: FALSE Diff: 1 Page Ref: 155 Section Heading: A Blend Example Keywords: blending AACSB: Analytical thinking 21) Data envelopment analysis problems are usually maximization problems. Answer: TRUE Diff: 1 Page Ref: 165 Section Heading: A Data Envelopment Analysis Example Keywords: data envelopment analysis AACSB: Application of knowledge 22) Double-subscripted variables are required when there are two decision variables. Answer: FALSE Diff: 1 Page Ref: 153 Section Heading: A Transportation Example Keywords: double-subscripted AACSB: Application of knowledge 23) A company can use regular time, overtime, and subcontracting in any amount over the oneyear production planning horizon to meet forecasted demand. If they develop the plan using linear programming, they will have a total of 36 decision variables that govern the amount produced by these three methods. Answer: TRUE Diff: 2 Page Ref: 160-164 Section Heading: A Multiperiod Scheduling Example Keywords: formulation, constraints AACSB: Analytical thinking 24) A data envelopment analysis with an objective function value of 0.8 means the company is more efficient than its competitors since it expends only 80% of the effort to achieve the same results. Answer: FALSE Diff: 2 Page Ref: 168 Section Heading: A Data Envelopment Analysis Example Keywords: data envelopment analysis AACSB: Application of knowledge 4 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 25) Data envelopment analysis indicates the relative ________ of a service unit compared with others. Answer: efficiency or productivity Diff: 2 Page Ref: 165 Section Heading: A Data Envelopment Analysis Example Keywords: data envelopment analysis AACSB: Application of knowledge 26) ________ types of linear programming problems often result in fractional relations between variables which must be eliminated. Answer: Blending Diff: 2 Page Ref: 156-160 Section Heading: A Blend Example Keywords: blending AACSB: Application of knowledge 27) Cranky Jerry's Furniture Factory makes tables and chairs. If he is interested in a profit maximizing level of production, he should probably follow the example for the ________ problem found in this chapter. Answer: product mix Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: product mix AACSB: Application of knowledge 28) When the ________ command is used in an Excel spreadsheet, all the values in a column (or row) are multiplied by the values in another column (or row) and then summed. Answer: SUMPRODUCT Diff: 2 Page Ref: 140-143 Section Heading: A Diet Example Keywords: spreadsheet solution AACSB: Application of knowledge 29) Cranky Jerry's Day Care wants to minimize their food cost while meeting the minimum (and I mean bare minimum) guidelines for nutrition as set forth by the state. The best approach would be to follow the example in this chapter for a(n) ________ problem. Answer: diet Diff: 2 Page Ref: 140-143 Section Heading: A Diet Example Keywords: diet example AACSB: Application of knowledge 5 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 30) The ________ for the computer solution of a linear programming problem requires all variables on the left side, and all numerical values on the right side of the inequality or equality sign. Answer: standard form Diff: 2 Page Ref: 144 Section Heading: An Investment Example Keywords: formulation, constraints AACSB: Application of knowledge 31) The objective function of a diet problem is usually to ________ subject to nutritional requirements. Answer: minimize costs Diff: 1 Page Ref: 140-143 Section Heading: A Diet Example Keywords: diet problem AACSB: Analytical thinking 32) Investment problems maximize ________. Answer: return on investments Diff: 1 Page Ref: 143-147 Section Heading: An Investment Example Keywords: investment AACSB: Application of knowledge 33) In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the ________. Answer: audience exposure Diff: 2 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: marketing problem, media selection AACSB: Analytical thinking 34) In a(n) ________ problem, maximization of audience exposure may not result in maximization of total profit. Answer: media selection Diff: 3 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: marketing problem, media selection AACSB: Application of knowledge 35) In a balanced transportation model, supply equals ________. Answer: demand Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Application of knowledge 6 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 36) A balanced transportation model should have ________ constraints. Answer: = or "equal to" Diff: 2 Page Ref: 153 Section Heading: A Transportation Example Keywords: transportation problem, formulation AACSB: Analytical thinking 37) There are three plants scattered across the United States that manufacture Dull computers. These plants assemble products for customers throughout the United States, Canada, and Mexico. If Dull wishes to maximize profit by choosing the most economical pair of factory and customer for each order, they would be well-advised to follow the ________ model presented in this chapter. Answer: transportation problem Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: transportation model AACSB: Application of knowledge 38) In a data envelopment analysis, it is customary to scale input process so that the total value of a unit's inputs equals ________. Answer: one Diff: 1 Page Ref: 166 Section Heading: A Data Envelopment Analysis Example Keywords: data envelopment analysis AACSB: Application of knowledge 39) When systematically formulating a linear program, the first step is to: A) construct the objective function. B) formulate the constraints. C) identify the decision variables. D) identify the parameter values. Answer: C Diff: 2 Page Ref: 135 Section Heading: A Product Mix Example Keywords: formulation AACSB: Application of knowledge 7 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 40) Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York Stock Exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock 2." The constraint for this requirement can be written as: A) x2 ≥ .60. B) x2 ≥ .60 (x2 + x7 + x8). C) .4x2 - .6x7 - .6x8 ≤ 0. D) .4x2 - .6x7 - .6x8 ≥ 0. Answer: C Diff: 3 Page Ref: 143-147 Section Heading: An Investment Example Keywords: formulation AACSB: Analytical thinking 41) The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B, which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient. Ingredient 1 2 3 4 5 Percent per pound Percent per pound in Feed A in Feed B 20 24 30 10 0 30 24 15 10 20 Minimum daily requirement (pounds) 30 50 20 60 40 The constraint for ingredient 3 is: A) .5A + .75B = 20. B) .3B = 20. C) .3B ≤ 20. D) .3B ≥ 20. Answer: D Diff: 2 Page Ref: 140-143 Section Heading: A Diet Example Keywords: solution AACSB: Analytical thinking 8 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Artisanal Chips The owner of Artisanal Chips etc. produces three flavors of artisanal corn chips marketed at new college graduates — pumpkin (P), chipotle adobo (A) and basement (B). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 1,000 ounces of salt, 2,000 ounces of maize, and 1,200 ounces of herbs. A bag of pumpkin chips requires 2 ounces of salt, 6 ounces of maize, and 1.75 ounces of herbs to produce; while a bag of chipotle-adobo chips requires 6 ounces of salt, 6 ounces of maize, and 5 ounces of herbs. A bag of basement chips requires 1.75 ounces of salt, 3.5 ounces of maize, and 1.5 ounces of herbs. Profits for a bag of basement chips are $0.40, for chipotle-adobo chips is $0.60, and for a bag of pumpkin chips $0.50. 42) For the production combination of 100 bags of each flavor of chips, which of the three resources is (are) not completely used? A) maize only B) salt and maize only C) herbs maize and salt D) salt and herbs only Answer: C Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: solution, slack AACSB: Analytical thinking 43) What is the constraint for salt? A) 2P + 6C + 1.75B ≤ 1000 B) 2P + 3C + 4B ≤ 1000 C) 3P + 6C + 3.5B ≤ 2000 D) 3P + 3C + 4B ≤ 2000 Answer: A Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: formulation, constraints AACSB: Analytical thinking 44) Which of the following is not a feasible production combination? A) 128B and 128C B) 128C and 128P C) 128P and 128B D) 150P, 10C and 360B Answer: B Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: formulation, feasibility AACSB: Analytical thinking 9 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 45) Which of these answers is optimal? A) 120P, 100C, and 88B B) 130P, 88C and 100B C) 140P, 88C and 88B D) 150P and 400B Answer: D Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: formulation, feasibility AACSB: Analytical thinking Taco Quatro Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas. A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. 46) What is an appropriate objective function for this fast food vignette? A) Max Z = 2.75N + 4B + 2Q + 3E B) Min Z = 400C + 150M + 400B + 250T C) Min Z = 2.75N + 4B + 2Q + 3E D) Max Z = 400C + 150M + 400B + 250T Answer: A Diff: 1 Page Ref: 136 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking 47) Which of these is a decision variable for the LP formulation of this problem? A) cheese B) Nacholupa C) 400 D) $2.75 Answer: B Diff: 1 Page Ref: 135 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking 10 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 48) What is an appropriate constraint for this fast food vignette? A) 250T + 400B + 150M + 400C B) 4C + 1M + 0B + 4T ≤ 4 C) 2N + 4B + 4Q + 3E ≤ 400 D) 2.75N + 4B + 2Q + 3E Answer: C Diff: 1 Page Ref: 136 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking 49) How many decision variables are in the LP formulation? A) 1 B) 2 C) 3 D) 4 Answer: D Diff: 1 Page Ref: 135 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking 50) Which of these statements about the sensitivity report is best? Cell $D$4 $C$4 Final Name Value Burritaco 0 Nacholupa 55 Reduced Cost -0.125 0 Objective Coefficient 4 2.75 Allowable Increase 0.125 0.25 Allowable Decrease 1E+30 0.114 A) There are no Burritacos being made. B) If the Nacholupa has a cost reduction of more than 0, none will be made. C) The company can make up to 1E + 30 Burritacos. D) The company can make an additional 0.25 Nacholupas if they want to with the leftover ingredients. Answer: A Diff: 1 Page Ref: 136-138 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking 11 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 51) Which of the statements about this portion of the sensitivity report is best? Cell $G$7 $G$8 Name Cheese Meat Final Value 400 150 Shadow Price 0.25 0.125 Constraint R.H. Side 400 150 Allowable Allowable Increase Decrease 16.66667 233.3333 110 10 A) Cheese costs more than meat. B) One additional pound of meat should be purchased if it can be acquired for $2 or less. C) There is both cheese and meat left over if the optimal product mix is produced. D) The shadow price of cheese can rise to 16.8167 before the right hand side changes. Answer: B Diff: 1 Page Ref: 136-138 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking 12 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Atwitter The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and Facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Newspaper Radio Twitter Facebook Exposure 5,000 3,000 700 200 Cost $500 $250 $25 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140-character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) 52) What is an appropriate objective function for this scenario? A) Max Z = 5,000N + 3,000R + 700T + 200F B) Max Z = 500N + 250R + 125T + 15F C) Min Z = 500N + 250R + 125T + 15F D) Min Z = 5,000N + 3,000R + 700T + 200F Answer: A Diff: 1 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking 53) Which of these is an appropriate constraint for this scenario? A) 5,000N + 3,000R + 700T + 200F ≤ 3,500 B) 500N + 250R + 125T + 15F ≤ 3,500 C) N + R + T + F ≥ 36 D) T ≤ 2,800 Answer: B Diff: 1 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking 13 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 54) A portion of the variable cells section of the sensitivity report in Excel appears in the table below. How many potential customers will be reached by the optimal advertising campaign? Cell $C$2 $D$2 $E$2 $F$2 Name Newspaper Radio Twitter Facebook Final Value 0 13.76 0 4 Reduced Cost -1000 0 -800 0 Objective Coefficient 5000 3000 700 200 A) 17.76 B) 8,900 C) 42,080 D) cannot be determined from the sensitivity report Answer: C Diff: 1 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking 55) Which of these statements about the sensitivity report for the constraints is best? Cell $G$5 Name Budget Final Value 3500 Shadow Price 12 Constraint R.H. Side 3500 Allowable Increase 2560 Allowable Decrease 3440 A) Only $940 of the advertising budget is being spent on this campaign. B) The advertising campaign needs another $2,560 to reach the maximum number of customers. C) It is possible to reach enough customers by spending only $60. D) For every $1 increase in the budget, the ad campaign can reach twelve more customers. Answer: D Diff: 1 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking 14 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 56) What is the proper interpretation of the shadow price for Facebook? Cell $G$9 Name Facebook Final Value 4 Shadow Price 20 Constraint R.H. Side 4 Allowable Increase 229.3333 Allowable Decrease 4 A) Every additional dollar spent on Facebook advertising gains 20 customers as long as the number of postings does not exceed 233. B) Every additional dollar spent on Facebook advertising gains 20 customers as long as the number of postings does not exceed 229. C) If they spend $4, then can reach 20 customers. D) If they spend less than $20, they can reach 229.333 customers. Answer: A Diff: 1 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking 57) How should the entry for the Newspaper decision variable be interpreted? Cell $C$2 Name Newspaper Final Value 0 Reduced Cost -1000 Objective Coefficient 5000 Allowable Increase 1000 Allowable Decrease 1E+30 A) The director should lower the newspaper advertising expense by $1,000 to reach the objective of 5,000 customers contacted. B) If the director were forced to purchase a newspaper advertisement, he would reach 1000 fewer customers than would be reached using the optimal advertising campaign. C) If the director increased newspaper advertisement by 1,000, he would spend $1000 less than with the current campaign. D) It is possible to reach an almost infinite fewer number (10 to the 30th power) of customers by newspaper than by any other method. Answer: B Diff: 1 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: objective function, model formulation AACSB: Analytical thinking 15 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 58) If Xab = the production of product a in period b, then to indicate that the limit on production of the company's 3 products in period 2 is 400, we write: A) X32 ≤ 400. B) X21 + X22 + X23 ≤ 400. C) X12 + X22 + X32 ≤ 400. D) X12 + X22 + X32 ≥ 400. Answer: C Diff: 2 Page Ref: 160-164 Section Heading: A Multiperiod Scheduling Example Keywords: formulation, constraints AACSB: Analytical thinking 59) Balanced transportation problems have which of the following type of constraints? A) ≥ B) ≤ C) = D) < Answer: C Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: formulation, constraints AACSB: Application of knowledge 60) Compared to blending and product mix problems, transportation problems are unique because: A) they maximize profit. B) the constraints are all equality constraints with no "≤" or "≥" constraints. C) they contain fewer variables. D) the solution values are always integers. Answer: D Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: transportation AACSB: Application of knowledge 16 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 61) A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. What is the optimal daily profit? A) $380 B) $400 C) $420 D) $440 Answer: A Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: computer solution AACSB: Analytical thinking 17 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament. The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs. Bird Eggs/week Plumage Temperament Fertilizer Appetite Leghorn 5 3 2 3 5 Cochin 2 9 8 2 4 Buff Orpington 4.5 6 5 4 8 Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. 62) Which of the following is an appropriate objective function? A) Max Z = 5L + 2C + 4.5B B) Max Z = 10L + 10C + 10B C) Min Z = 5L + 2C + 4.5B D) Min Z = 10L + 10C + 10B Answer: A Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: objective, cost minimization, profit maximization AACSB: Analytical thinking 63) The poultry farmer would like to generate 80 ounces of fertilizer per week while feeding a maximum of 160 ounces of layer pellets each week. Which of these constraints is correct? A) 3L + 2C + 4C ≤ 80 B) 5L + 4C + 8B ≤ 160 C) 5L + 4C + 8B ≥ 160 D) 5L + 4C + 8B ≥ 80 Answer: B Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: constraint, model formulation AACSB: Analytical thinking 18 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 64) The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. When he runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He can picture the sad little faces of his children when he tells them that there will be no variety of birds gracing their front lawn this summer. Help him avoid the embarrassment by selecting a constraint that will ensure that there is some variety in his flock. A) 5L + 4C + 8B ≤ 160 B) 5L + 4C + 8B ≥ 160 C) C + B ≥ 5 D) L + C + B ≥ 5 Answer: C Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: constraints, formulation AACSB: Analytical thinking 65) When the poultry farmer runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He studies his sensitivity report (copied below) and decides to write a constraint that requires two Cochin chickens to be selected. If the current optimal mix of breeds results in 160 eggs per week, which of the following statements is best? Cell $B$1 $C$1 $D$1 Objective Allowable Allowable Name Final Value Reduced Cost Coefficient Increase Decrease Leghorn 32 0 5 1E+30 2.1875 Cochin 0 -2 2 3 1E+30 Buff Orpington 0 -3.5 4.5 3.5 1E+30 A) The new weekly egg output will be 169. B) The new weekly egg output will be 162. C) The new weekly egg output will be 158. D) The new weekly egg output will be 153. Answer: D Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: constraint, model formulation AACSB: Analytical thinking 19 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 66) The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. Use this portion of the sensitivity report to evaluate the following statements: Cell $B$1 $C$1 $D$1 Final Name Value Leghorn 32 Cochin 0 Buff Orpington 0 Reduced Cost 0 -2 -3.5 Objective Coefficient 5 2 4.5 Allowable Increase 1E+30 3 3.5 Allowable Decrease 2.1875 1E+30 1E+30 A) The noise level around the farm should be over 60 decibels. B) The fertilizer generated will be 160 ounces per week. C) Layer pellets will be consumed at the rate of 96 ounces per week. D) The plumage score will be less than 40. Answer: A Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: sensitivity analysis, right-hand-side value AACSB: Analytical thinking 67) Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the supply constraint for component 1. A) x21 + x22 ≤ 8000 B) x12 + x22 ≥ 8000 C) x11 + x12 ≤ 8000 D) x21 + x22 ≥ 8000 Answer: C Diff: 2 Page Ref: 156-160 Section Heading: A Blend Example Keywords: formulation AACSB: Analytical thinking 20 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 68) Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the demand constraint for gasoline type 1. A) x21 + x22 = 11000 B) x12 + x22 = 11000 C) x11 + x21 ≤ 11000 D) x11 + x21 = 11000 Answer: D Diff: 2 Page Ref: 156-160 Section Heading: A Blend Example Keywords: formulation AACSB: Analytical thinking 69) Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the constraint stating that the component 1 cannot account for more than 35% of the gasoline type 1. A) x11 + x12 (.35)(x11 + x21) B) x11 + .35(x11 + x12) C) -.65x11 + .35x21 ≤ 0 D) .65x11 - .35x21 ≤ 0 Answer: D Diff: 3 Page Ref: 156-160 Section Heading: A Blend Example Keywords: formulation AACSB: Analytical thinking 70) Quickbrush Paint Company is developing a linear program to determine the optimal quantities of ingredient A and ingredient B to blend together to make oil-base and water-base paint. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. Assuming that x represents the number of gallons of oil-base paint, and y represents the gallons of waterbase paint, which constraint correctly represents the constraint on ingredient A? A) .9A + .1B ≤ 10,000 B) .9x + .1y ≤ 10,000 C) .3x + .7y ≤ 10,000 D) .9x + .3y ≤ 10,000 Answer: D Diff: 2 Page Ref: 156-160 Section Heading: A Blend Example Keywords: blending AACSB: Analytical thinking 21 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 71) A systematic approach to model formulation is to first: A) construct the objective function. B) develop each constraint separately. C) define decision variables. D) determine the right hand side of each constraint. Answer: C Diff: 2 Page Ref: 135 Section Heading: A Product Mix Example Keywords: model formulation AACSB: Application of knowledge 72) Let: rj = regular production quantity for period j, oj = overtime production quantity in period j, ij = inventory quantity in period j, and dj = demand quantity in period j. Correct formulation of the demand constraint for a multiperiod scheduling problem is: A) rj + oj + i2 - i1 ≥ dj. B) rj + oj + i1 - i2 ≥ dj. C) rj + oj + i1 - i2 ≤ dj. D) rj - oj - i1 + i2 ≥ dj. Answer: A Diff: 2 Page Ref: 160-164 Section Heading: A Multiperiod Scheduling Example Keywords: formulation, constraints AACSB: Analytical thinking 73) In a multiperiod scheduling problem, the production constraint usually takes the form of: A) beginning inventory + demand - production = ending inventory. B) beginning inventory - demand + production = ending inventory. C) beginning inventory - ending inventory + demand = production. D) beginning inventory + demand + production = ending inventory. Answer: B Diff: 2 Page Ref: 160-164 Section Heading: A Multiperiod Scheduling Example Keywords: model formulation, multiperiod scheduling problem AACSB: Analytical thinking 74) The type of linear program that compares services to indicate which one is less productive or inefficient is called: A) product mix. B) data envelopment analysis. C) marketing. D) blending. Answer: B Diff: 2 Page Ref: 165 Section Heading: A Data Envelopment Analysis Example Keywords: formulation AACSB: Application of knowledge 22 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. 75) The stockbroker suggests limiting the investments so that no more than $10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350, whichever is more restrictive. How would this be formulated as a linear programming constraint? A) X2 ≤ 10000 X2 + X3 ≤ 350 B) 10,000 X2 ≤ 350X2 + 350X3 C) 47.25X2 ≤ 10,000 X2 + X3 ≤ 350 D) 47.25X2 ≤ 10,000 47.25 X2 + 110X3 ≤ 350 Answer: C Diff: 2 Page Ref: 143-147 Section Heading: An Investment Example Keywords: investment AACSB: Analytical thinking 76) An appropriate part of the model would be: A) 15X1 + 47.25X2 + 110 X3 ≤ 50,000. B) MAX 15X1 + 47.25X2 + 110X3. C) X1 + X2 +X3 ≤ 50,000. D) MAX 50(15)X1 + 50 (47.25)X2 + 50 (110)X3. Answer: A Diff: 2 Page Ref: 143-147 Section Heading: An Investment Example Keywords: investment AACSB: Analytical thinking 77) The expected returns on investment of the three stocks are 6%, 8%, and 11%. An appropriate objective function is: A) MAX .06X1 +.08X2 +.11X3. B) MAX .06(15)X1 +.08(47.25)X2 +.11(110)X3. C) MAX 15X1 + 47.25X2 +.110X3. D) MAX (1/.06)X1 +.(1/08)X2 + (1/.11)X3. Answer: B Diff: 2 Page Ref: 143-147 Section Heading: An Investment Example Keywords: investment AACSB: Analytical thinking 23 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 78) The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct? A) X1 ≤ 0.35 B) X1 = 0.35 (50000) C) X1 ≤ 0.35(X1 + X2 + X3) D) X1 = 0.35(X1 + X2 + X3) Answer: C Diff: 2 Page Ref: 143-147 Section Heading: An Investment Example Keywords: investment AACSB: Analytical thinking ABC123 45 records are produced by Jackson Enterprises at three different locations, 1, 2, and 3, and shipped to three sales centers named A, B and C. Company creative director Michael is unconcerned with efficiency, but operations manager Tito wishes to move the product as inexpensively as possible. The cost to transport one crate from each source to each destination is indicated in the table. as well as the demand at each sales center and the supply at each manufacturing facility. 1 2 3 Total demand A $5 $6 $7 400 B $6 $9 $4 400 C Total Supply $7 320 $8 420 $6 520 460 79) Which of these is an appropriate constraint for the problem? A) x1A + x1B +x1C = 320 B) x1A + x2A +x3A = 320 C) x3A + x3B +x3C = 460 D) x1B + x2B +x3B = 420 Answer: A Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: computer solution, transportation/distribution AACSB: Analytical thinking 24 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 80) What is the optimal answer to this problem? A) $7202 B) $7120 C) $7220 D) $7320 Answer: B Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: computer solution, transportation/distribution AACSB: Analytical thinking 81) Suppose demand in sales center C drops to 400 units while demand in centers A and B both increase to 430. How does the problem formulation change? A) All of the constraints become less than or equal to constraints. B) Only the supply constraints become less than or equal to constraints. C) Only the demand constraints become less than or equal to constraints. D) The constraints do not change. Answer: D Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: computer solution, transportation/distribution AACSB: Analytical thinking 82) Suppose demand in sales center C drops to 400 units. How does the problem formulation change and what is the optimal answer? Answer: The supply constraints become "less than or equal to" constraints and the total amount shipped to location C must now equal 400. All of the demand constraints are "equal to" constraints to force the model to ship product. MIN Z = 5x1A + 6x1B + 7x1C + 6x2A + 9x2B + 8x2C + 7x3A + 4x3B + 6x3C s.t. x1A + x1B +x1C ≤ 320 x2A + x2B +x2C ≤ 420 x3A + x3B +x3C ≤ 520 x1A + x2A +x3A = 400 x1B + x2B +x3B = 400 x1C + x2C +x3C = 400 The solution has a total cost of $6,640 and sends 40 units from 1 to A, 280 units from 1 to C, 360 units from 2 to A, 400 units from 3 to B, and 120 units from 3 to C. Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: computer solution, transportation/distribution AACSB: Analytical thinking 25 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Artisanal Chips The owner of Artisanal Chips etc. produces three flavors of artisanal corn chips marketed at new college graduates — pumpkin (P), chipotle adobo (A) and basement (B). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 1,000 ounces of salt, 2,000 ounces of maize, and 1,200 ounces of herbs. A bag of pumpkin chips requires 2 ounces of salt, 6 ounces of maize, and 1.75 ounces of herbs to produce; while a bag of chipotle-adobo chips requires 6 ounces of salt, 6 ounces of maize, and 5 ounces of herbs. A bag of basement chips requires 1.75 ounces of salt, 3.5 ounces of maize, and 1.5 ounces of herbs. Profits for a bag of basement chips are $0.40, for chipotle-adobo chips is $0.60, and for a bag of pumpkin chips $0.50. 83) What is the formulation for this problem? Answer: MAX Z = 0. 5P + 0.6C + 0.4B s.t. 2P + 6C + 1.75B ≤ 1000 3P + 6C + 3.5B ≤ 2000 4P + 5C + 1.5B ≤ 1200 Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: computer solution AACSB: Analytical thinking 84) For the production combination of 16 pumpkin, 125 chipotle-adobo, and 124 basement, which resource is not completely used up and how much is remaining? Answer: 1 ounce salt, 325 ounces herbs, and 768 ounces maize Diff: 1 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: slack, computer solution AACSB: Analytical thinking 85) The production combination of 180 bags of pumpkin and 100 bags of chipotle-adobo is not feasible because one resource is exceeded. Which resource is exceeded and how much more is needed to produce this combination? Answer: Herbs only, 20 ounces are needed Diff: 1 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: slack, computer solution AACSB: Analytical thinking 86) What is the optimal product mix and resulting profit? Answer: A profit of $235 is attainable if Artisanal Chips, Etc., produces 150 bags of pumpkin and 400 bags of basement flavored chips. Diff: 1 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: slack, computer solution AACSB: Analytical thinking 26 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons) of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. The shop must produce at least 400 almond-filled croissants due to customer demand. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. 87) This represents what type of linear programming application? Answer: product mix Diff: 1 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: computer solution AACSB: Application of knowledge 88) What is the formulation for this problem? Answer: MAX Z = $.20B + $.30C s.t. 6B + 3C ≤ 6600 1B + 1C ≤ 1400 2B + 4C ≤ 4800 C ≥ 400 Diff: 1 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: formulation, constraints AACSB: Analytical thinking 89) For the production combination of 600 bear claws and 800 almond-filled croissants, how much flour and almond paste are remaining? Answer: flour = 600 ounces, almond paste = 400 TS Diff: 1 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: slack, computer solution AACSB: Analytical thinking 90) If Xij = the production of product i in period j, write an expression to indicate that the limit on production of the company's three products in period 2 is 400. Answer: X12 + X22 + X32 ≤ 400 Diff: 2 Page Ref: 160-164 Section Heading: A Multiperiod Scheduling Example Keywords: transportation problem, supply constraint AACSB: Analytical thinking 27 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Atwitter The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and Facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Newspaper Radio Twitter Facebook Exposure 5,000 3,000 700 200 Cost $500 $250 $25 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140-character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) 91) Formulate the appropriate objective function for this scenario. Answer: Max Z = 5,000x1 + 3,000x2 + 700x3 + 200x4 Where x1 = Newspaper advertisements x2 = Radio advertisements x3 = Tweets x4 = Facebook postings Diff: 2 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: linear programming formulation AACSB: Analytical thinking 28 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 92) Formulate the appropriate LP model for this scenario. Answer: Max Z = 5,000x1 + 3,000x2 + 700x3 + 200x4 Where x1 = Newspaper advertisements x2 = Radio advertisements x3 = Tweets x4 = Facebook postings Subject to: $500x1 + $250x2 + $125x3 + $15x4 ≤ $3,500 x1 ≤ 4 x2 ≤ 24 x3 ≤ 3 x4 ≤ 4 Diff: 2 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: linear programming formulation AACSB: Analytical thinking 93) The Excel LP model for this scenario shows the following sensitivity report for the variable cells. Comment on the salient features. Cell $C$2 $D$2 $E$2 $F$2 Name Newspaper Radio Twitter Facebook Final Value 0 13.76 0 4 Reduced Cost -1000 0 -800 0 Objective Coefficient 5000 3000 700 200 Allowable Increase 1000 333.3333 800 1E+30 Allowable Decrease 1E+30 500 1E+30 2 Answer: The model recommends four Facebook postings and almost 14 radio spots which will reach 42,080 potential tourists. Forcing the two unchosen media would result in a drop of 1000 customers if newspaper entered the marketing mix and a drop of 800 customers if Twitter was required. The Facebook allowable decrease is of some concern among all shown as the decrease of 2 units is small by comparison to the other ranges shown for the newspaper, radio and Twitter channels. Diff: 2 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: linear programming formulation AACSB: Analytical thinking 29 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 94) The Excel LP model for this scenario shows the following sensitivity report for the constraints. Comment on the salient features. Cell $G$5 $G$6 $G$7 $G$8 $G$9 Name Budget Newspaper Radio Twitter Facebook Final Value 3500 0 13.76 0 4 Shadow Price 12 0 0 0 20 Constraint R.H. Side 3500 4 24 3 4 Allowable Increase 2560 1E+30 1E+30 1E+30 229.3333333 Allowable Decrease 3440 4 10.24 3 4 Answer: The budget has a shadow price of 12, meaning that for every $1 increase in budget, an additional 12 customers could be reached. Facebook's shadow price of 20 can be interpreted as an increase in 20 customers receiving the message for each additional Facebook posting up to 233 postings. Newspaper and Twitter are not in the model and thus have no opportunity cost in this formulation. The budget shadow price is robust, but that of Facebook is comparatively narrow. Diff: 2 Page Ref: 148-152 Section Heading: A Marketing Example Keywords: linear programming formulation AACSB: Analytical thinking 30 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 ABC123 45 records are produced by Jackson Enterprises at three different locations, 1, 2, and 3, and shipped to three sales centers named A, B and C. Company creative director Michael is unconcerned with efficiency, but operations manager Tito wishes to move the product as inexpensively as possible. The cost to transport one crate from each source to each destination is indicated in the table. as well as the demand at each sales center and the supply at each manufacturing facility. 1 2 3 Total demand A $5 $6 $7 400 B $6 $9 $4 400 C Total Supply $7 320 $8 420 $6 520 460 95) Write the formulation for this problem. Answer: MIN Z = 5x1A + 6x1B + 7x1C + 6x2A + 9x2B + 8x2C + 7x3A + 4x3B + 6x3C s.t. x1A + x1B +x1C = 320 x2A + x2B +x2C = 420 x3A + x3B +x3C = 520 x1A + x2A +x3A = 400 x1B + x2B +x3B = 400 x1C + x2C +x3C = 460 Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: computer solution, transportation/distribution AACSB: Analytical thinking 96) What is the optimal answer to this problem? Answer: 320 units from 1 to A 80 units from 2 to A 340 units from 2 to C 400 units from 3 to B 120 units from 3 to C total cost of $7,120 Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: computer solution, transportation/distribution AACSB: Analytical thinking 31 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 97) Suppose demand in sales center C drops to 400 units. How does the problem formulation change? Answer: The supply constraints become "less than or equal to" constraints and the total amount shipped to location C must now equal 400. All of the demand constraints are "equal to" constraints to force the model to ship product. MIN Z = 5x1A + 6x1B + 7x1C + 6x2A + 9x2B + 8x2C + 7x3A + 4x3B + 6x3C s.t. x1A + x1B +x1C ≤ 320 x2A + x2B +x2C ≤ 420 x3A + x3B +x3C ≤ 520 x1A + x2A +x3A = 400 x1B + x2B +x3B = 400 x1C + x2C +x3C = 400 Diff: 2 Page Ref: 153-155 Section Heading: A Transportation Example Keywords: computer solution, transportation/distribution AACSB: Analytical thinking 98) Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-base paint to produce to maximize its total profit. How much oil-based and water-based paint should the Quickbrush make? Answer: 9167 gallons of water-base paint and 5833 gallons of oil-base paint Diff: 2 Page Ref: 156-160 Section Heading: A Blend Example Keywords: blending AACSB: Analytical thinking 32 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Andy Tyre manages Tyre's Wheels, Inc. Andy has received an order for 1000 standard wheels and 1200 deluxe wheels for next month, and for 750 standard wheels and 1000 deluxe wheels the following months. He must fill all the orders. The cost of regular time production for standard wheels is $25 and for deluxe wheels, $40. Overtime production costs 50% more. For each of the next two months there are 1000 hours of regular time production and 500 hours of overtime production available. A standard wheel requires .5 hour of production time and a deluxe wheel, .6 hour. The cost of carrying a wheel from one month to the next is $2. 99) Define the decision variables and objective function for this problem. Answer: Define the decision variables: S1R = number of standard wheels produced in month 1 on regular time production S1O = number of standard wheels produced in month 1 on overtime production S2R = number of standard wheels produced in month 2 on regular time production S2O = number of standard wheels produced in month 2 on overtime production D1R = number of deluxe wheels produced in month 1 on regular time production D1O = number of deluxe wheels produced in month 1 on overtime production D2R = number of deluxe wheels produced in month 2 on regular time production D2O = number of deluxe wheels produced in month 2 on overtime production Y1 = number of standard wheels stored from month 1 to month 2. Y2 = number of deluxe wheels stored from month 1 to month 2. MIN 25 S1R + 37.5 S1O + 40 D1R + 60 D1O + 25 S2R + 37.5 S2O + 40 D2R + 60 D2O + 2 Y1 + 2 Y2 Diff: 2 Page Ref: 160-164 Section Heading: A Multiperiod Scheduling Example Keywords: linear programming multiperiod scheduling AACSB: Analytical thinking 100) Write the constraints for this problem. Answer: S1R + S1O - Y1 = 1000 .5 S1R + .6 D1R ≤ 1000 D1R + D1O - Y2 = 1200 .5 S1O + .6 D1O ≤ 500 S2R + S2O + Y1 = 750 .5 S2R + .6 D2R ≤ 1000 D2R + D2O + Y2 = 1000 .5 S2O + .6 D12O ≤ 500 Diff: 2 Page Ref: 160-164 Section Heading: A Multiperiod Scheduling Example Keywords: linear programming multiperiod scheduling AACSB: Analytical thinking 33 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Bullseye Shirt Company makes three types of shirts: athletic, varsity, and surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4000 yards of cotton and 3000 yards of rayon per week. The table below shows relevant manufacturing information: Total Yards of Shirt Fabric per Shirt Athletic 1.00 Varsity 1.20 Surfer 0.90 Fabric Requirement at least 60% cotton no more than 30% rayon as much as 80% cotton Minimum Weekly Contracts 500 650 300 Maximum Selling Demand Price 600 $30 850 $40 700 $36 Assume that the decision variables are defined as follows: A = total number of athletic shirts produced V = total number of varsity shirts produced S = total number of surfer shirts produced C = yards of cotton purchased R = yards of rayon purchased Xij = yards of fabric i (C or R) blended into shirt j (A, V or S) 101) Write the objective function. Answer: max 30 A + 40 V + 36 S - 5C - 7R Diff: 2 Page Ref: 156-160 Section Heading: A Blend Example Keywords: objective function, model construction AACSB: Analytical thinking 102) Write the constraints for the fabric requirements. Answer: Form of constraints: Total yards used is greater than (or less than) total yards required × (% fabric required) shirts produced. XCA ≥ 0.6 A XVR ≤ 0.36V XSC ≤ 0.72 S Diff: 2 Page Ref: 156-160 Section Heading: A Blend Example Keywords: blending AACSB: Analytical thinking 34 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 103) Write the constraints for the total number of shirts of each style produced. Answer: Form of constraint: number of shirts produced = (total yards used to make the shirt)/(yards/shirt) A = (XCA + XRA)/1 V = (XCV + XRV)/1.2 S = (XCS + XRS)/0.9 Standard form: A - XCA - XRA = 0 1.2 V - XCV - XRV = 0 0.9 S - XCS - XRS = 0 Diff: 3 Page Ref: 156-160 Section Heading: A Blend Example Keywords: blending AACSB: Analytical thinking 104) Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel's cat food is made by mixing two types of cat food to obtain the "nutritionally balanced cat diet." The data for the two cat foods are as follows: Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the cost of this plan, and how much fat and protein do the cats receive? Answer: Cost is $3.60, which uses 14 ounces of Meow Munch and 5.33 ounces of Feline Feed. Diff: 2 Page Ref: 140-143 Section Heading: A Diet Example Keywords: diet AACSB: Analytical thinking 35 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament. The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs. Bird Eggs/week Plumage Temperament Fertilizer Appetite Leghorn 5 3 2 3 5 Cochin 2 9 8 2 4 Buff Orpington 4.5 6 5 4 8 Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. 105) How should the objective function read? Answer: Max Z = 5L + 2C + 4.5B Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: objective function AACSB: Analytical thinking 106) What is a full set of constraints if the farmer wants this flock to produce less than 100 decibels of noise and more than 5 pounds of fertilizer, consume less than 10 pounds of layer pellets, and achieve a total plumage score of at least 75? Answer: 3L + 9C+ 6B > = 75 2L + 8C + 5B <= 100 3L + 2C + 4B >= 80 5L + 4C + 8B <= 160 Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: constraints, formulation AACSB: Analytical thinking 36 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 107) Formulate the objective function and constraints for this scenario. Answer: Max Z = 5L + 2C + 4.5B 3L + 9C+ 6B >= 75 Subject to: 2L + 8C + 5B <= 100 3L + 2C + 4B >= 80 5L + 4C + 8B <= 160 Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: formulation AACSB: Analytical thinking 108) The poultry farmer discovers, much to his dismay, that the product mix that satisfies all of his constraints isn't really a mix of birds–it's a flock consisting of nothing but 32 Leghorns. (His constraints were a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week.) Not only is his flock going to be a very one-note mix in terms of color, he is afraid that the gleaming white feathers and deafening noise will attract predators, or worse yet, his neighbors. He immediately embarks on a breeding program to develop a Super-Cochin that can lay 4.5 eggs per week with all other performance measures the same. His optimal solution is now 27.5 Leghorns and 5.625 Super-Cochins. Assuming that he is willing to settle for a flock that has 27 Leghorns and 5 Super Cochins, what is the weekly output of eggs and performance with respect to the constraints? Answer: He should get (27 × 5) + (4.5 × 5) = 157.5 eggs per week The plumage score is now 126. The fertilizer output is 91 ounces per week, The temperament score is 94. The appetite is 155 ounces of layer pellets per week. Diff: 2 Page Ref: 135-139 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking 37 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 109) A credit union wants to make investments in the following: The firm will have $2,500,000 available for investment during the coming year. The following restrictions apply: Risk-free securities may not exceed 30% of the total funds, but must comprise at least 5% of the total. Signature loans may not exceed 12% of the funds invested in all loans (vehicle, consumer, other secured loans, and signature loans). Consumer loans plus other secured loans may not exceed the vehicle loans. Other secured loans plus signature loans may not exceed the funds invested in risk-free securities. How should the $2,500,000 be allocated to each alternative to maximize annual return? What is the annual return? Answer: Diff: 3 Page Ref: 143-147 Section Heading: An Investment Example Keywords: investment AACSB: Analytical thinking 38 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Taco Quatro Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas. A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. 110) What is an appropriate objective function and constraints for this scenario? Answer: Max Z = 2.75N + 4B + 2Q + 3E subject to: Cheese 2N + 4B + 4Q + 3E ≤ 400 Meat 0N + 1B + 2Q + 2E ≤ 150 Beans 4N + 0B + 0Q + 2E ≤ 400 Tortilla 3N + 4B + 1Q + 3E ≤ 250 Diff: 3 Page Ref: 136 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking 111) What is an appropriate objective function for this scenario? Answer: Max Z = 2.75N + 4B + 2Q + 3E Diff: 2 Page Ref: 136 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking 39 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 112) The assistant manager had taken a management science class a few years before and while she knew enough to formulate the problem and implement it in Excel, the only sensitivity training she had ever received had to do with being more empathetic to the plight of her minimum wage workforce. Help her interpret the sensitivity report for the Nacholupa product as it appears below. Cell $C$4 Name Nacholupa Final Value 55 Reduced Cost 0 Objective Coefficient 2.75 Allowable Increase 0.25 Allowable Decrease 0.114 Answer: The optimal product mix calls for 55 Nacholupas to be prepared at a sale price of $2.75. This amount of Nacholupas would be optimal if the price rose by 25 cents up to $3 or dropped by 11.4 cents down to $2.636. Diff: 2 Page Ref: 138 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking 113) The assistant manager had taken a management science class a few years before and while she knew enough to formulate the problem and implement it in Excel, the only sensitivity training she had ever received had to do with being more empathetic to the plight of her minimum wage workforce. Help her interpret the sensitivity report for the cheese and meat constraints as it appears below. Cell $G$7 $G$8 Name Cheese Meat Final Value 400 150 Shadow Price 0.25 0.125 Constraint R.H. Side 400 150 Allowable Increase 16.66667 110 Allowable Decrease 233.33333 10 Answer: All 400 ounces of the cheese and 150 ounces of the meat are used in the optimal product mix. If the assistant manager could buy an ounce of cheese for 25 cents or less, they should do that up to an additional 16.6 ounces of cheese. If they were to waste cheese, each ounce lost would effectively lose them 25 cents up to losing 233 ounces. Additional meat should be purchased up to a price of 12.5 cents per ounce and up to an additional 110 ounces. Wasting an ounce of meat costs 12.5 cents per ounce up to a loss of 10 ounces. Diff: 2 Page Ref: 138 Section Heading: A Product Mix Example Keywords: product mix AACSB: Analytical thinking 40 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Introduction to Management Science, 13e, Global Edition (Taylor) Module B Transportation and Assignment Solution Methods 1) In a transportation problem, items are allocated from sources to destinations at a minimum cost. Answer: TRUE Diff: 1 Section Heading: Solution of the Transportation Model Keywords: transportation problem AACSB: Application of knowledge 2) The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination. Answer: TRUE Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem, linear prog model for a transportation problem AACSB: Application of knowledge 3) Transportation problems are solved manually within a tableau format. Answer: TRUE Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem AACSB: Application of knowledge 4) In a balanced transportation model where supply equals demand, all constraints are equalities. Answer: TRUE Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem, balanced transportation model AACSB: Application of knowledge 5) In a balanced transportation model where supply equals demand, all constraints are inequalities. Answer: FALSE Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem, balanced transportation model, constraints AACSB: Application of knowledge 6) The supply and demand values along the outside rim of a tableau are called rim requirements. Answer: TRUE Diff: 3 Section Heading: Solution of the Transportation Model Keywords: supply and demand values, rim requirements AACSB: Application of knowledge 1 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 7) Unacceptable (prohibited) routes in a transportation problem are assigned cost values of zero. Answer: FALSE Diff: 1 Section Heading: Solution of the Transportation Model Keywords: prohibited routes AACSB: Application of knowledge 8) An assignment problem is a special form of transportation problem where all supply and demand values equal 1. Answer: TRUE Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Application of knowledge 9) An assignment problem is a special form of transportation problem where all supply and demand values equal 0. Answer: FALSE Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Application of knowledge 10) An opportunity cost table is developed by first subtracting the minimum value in each row from all other row values and then repeating this process for each column. Answer: TRUE Diff: 3 Section Heading: Solution of the Assignment Model Keywords: opportunity cost table AACSB: Application of knowledge 11) An opportunity cost table is developed by first subtracting the minimum value in each row from all other row values and then repeating this process for each row. Answer: FALSE Diff: 3 Section Heading: Solution of the Assignment Model Keywords: opportunity cost table AACSB: Application of knowledge 12) Assignments are made to locations with 0 in the opportunity cost table. Answer: TRUE Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Application of knowledge 2 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 13) Assignments are made to locations with 1 in the opportunity cost table. Answer: FALSE Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Application of knowledge 14) An optimal solution occurs when the number of independent unique assignments equals the number of rows or columns. Answer: TRUE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: assignment problem, unique assignments AACSB: Application of knowledge 15) If the number of unique assignments is less than the number of rows or columns, a line test must be used. Answer: TRUE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: assignment problem, unique assignments AACSB: Application of knowledge 16) An assignment problem that involves 6 machines to be assigned to 4 workers cannot be solved using the assignment problem solution procedure described. Answer: FALSE Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Application of knowledge 17) The transportation model is a special type of linear regression model. Answer: FALSE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: transportation model AACSB: Application of knowledge 18) The transportation model assumes that shipping costs are the same, regardless of the number of units shipped. Answer: TRUE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: transportation model AACSB: Application of knowledge 3 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 19) It is not possible to solve a transportation problem that has ≤ instead of = signs for the supply constraints. Answer: FALSE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: transportation model AACSB: Application of knowledge 20) Transportation problems can be solved by the simplex method. Answer: TRUE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: transportation model AACSB: Application of knowledge 21) When the number of people and the number of tasks are not equal in an assignment problem then the problem cannot be solved. Answer: FALSE Diff: 1 Section Heading: Solution of the Assignment Model Keywords: assignment method AACSB: Application of knowledge 22) In the ________ method, the largest possible allocation is made to the cell in the upper-lefthand corner of the tableau, followed by allocations to adjacent feasible cells. Answer: northwest corner Diff: 2 Section Heading: Solution of the Transportation Model Keywords: northwest corner method AACSB: Application of knowledge 23) In using the minimum cell cost method, as much as possible is allocated to the cell with the ________ cost. Answer: minimum Diff: 1 Section Heading: Solution of the Transportation Model Keywords: minimum cell cost method AACSB: Application of knowledge 24) ________ model is a method for determining an initial solution for a transportation problem based on the concept of penalty cost or regret. Answer: Vogel's approximation Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method AACSB: Application of knowledge 4 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 25) In using the Vogel's Approximation model, a(n) ________ is the difference between the largest and next largest cell cost in a row. Answer: penalty cost Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method, penalty cost AACSB: Application of knowledge 26) Vogel's approximation method allocates to the minimum cost cell in the row or column with the ________ penalty cost. Answer: largest Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method, penalty cost AACSB: Application of knowledge 27) A multiple optimal solution occurs when an empty cell has a cost change of ________ and all other empty cells are positive. Answer: zero Diff: 2 Section Heading: Solution of the Transportation Model Keywords: stepping stone method, MODI AACSB: Application of knowledge 28) When demand exceeds supply, a dummy ________ is added to the solution tableau. Answer: row or supply Diff: 1 Section Heading: The Unbalanced Transportation Problem Keywords: unbalanced transportation problem AACSB: Application of knowledge 29) When supply exceeds demand, a dummy ________ is added to the solution tableau. Answer: column or destination Diff: 1 Section Heading: The Unbalanced Transportation Problem Keywords: unbalanced transportation problem AACSB: Application of knowledge 30) In a transportation tableau with m rows and n columns, if there are fewer than n+m-1 allocations, the tableau is said to be ________. Answer: degenerate Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: transportation tableau, degenerate solution AACSB: Application of knowledge 5 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 31) In a transportation tableau to rectify a degenerate tableau, an empty cell must artificially be treated as a(n) ________ cell. Answer: occupied or full Diff: 3 Section Heading: The Unbalanced Transportation Problem Keywords: degenerate solution, transportation tableau AACSB: Application of knowledge 32) A(n) ________ problem is a special form of transportation problem where all supply and demand values equal 1. Answer: assignment Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: assignment problem AACSB: Application of knowledge 33) A(n) ________ table is developed by first subtracting the minimum value in each row from all other row values and then repeating the process for each column. Answer: opportunity cost Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: opportunity cost table AACSB: Application of knowledge 34) A(n) ________ solution occurs when the number of independent unique assignments equals the number of rows or columns. Answer: optimal Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: optimal solution of the assignment problem, optimal assignments AACSB: Application of knowledge 35) The two solution methods for transportation problems that do not require the use of a computer are ________ and ________. Answer: stepping stone, MODI Diff: 1 Section Heading: The Unbalanced Transportation Problem Keywords: transportation problem solution methods AACSB: Application of knowledge 36) Generally, ________ problems match people to an equal number of tasks at a minimum cost. Answer: assignment Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: assignment AACSB: Application of knowledge 6 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 37) If the number of unique assignments is less than the number of rows, then a(n) ________ test must be used. Answer: line Diff: 2 Section Heading: The Unbalanced Transportation Problem Keywords: assignment AACSB: Application of knowledge 38) The three methods for identifying initial feasible solutions to transportation problems are ________, ________, and ________. Answer: northwest corner method, minimum cell cost method, Vogel's approximation method Diff: 1 Section Heading: The Unbalanced Transportation Problem Keywords: initial feasible solutions AACSB: Application of knowledge Given the following transportation tableau—where the numbers in each cell represent transportation costs from the specific source to the specific destination—with supply figures corresponding to each source and demand figures corresponding to each destination: 39) According to the Northwest Corner method, the initial solution would give to cell B2 a loading of ________. Answer: 150 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: northwest corner method AACSB: Analytical thinking 40) According to the Northwest Corner method, the initial solution would have a total transportation cost of ________. Answer: $2600 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: northwest corner method, total cost calculations AACSB: Analytical thinking 7 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 41) According to the Vogel's Approximation Method, the initial solution would give to cell B2 a loading of ________. Answer: 100 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method AACSB: Analytical thinking 42) According to the Vogel's Approximation Method, the initial solution would have a total transportation cost of ________. Answer: $2455 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method AACSB: Analytical thinking 43) According to the minimum cell cost method, the initial solution would give to cell C1 a loading of ________. Answer: 350 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: minimum cell cost method AACSB: Analytical thinking 44) According to the minimum cell cost method, the initial solution would have a total transportation cost of ________. Answer: $2455 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: minimum cell cost method AACSB: Analytical thinking 8 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Canning Transport wants to move goods from three (3) factories to three (3) distribution centers. Information about the move is given below: 45) According to the Northwest Corner method, the initial solution would give to cell CIII a loading of ________. Answer: 125 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: northwest corner method AACSB: Analytical thinking 46) According to the Northwest Corner method, the initial solution would have a total transportation cost of ________. Answer: $1800 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: northwest corner method AACSB: Analytical thinking 47) According to the Vogel's Approximation Method, the initial solution would give to cell CII a loading of ________. Answer: 0 or 25 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method AACSB: Analytical thinking 48) According to the Vogel's Approximation Method, the initial solution would have a total transportation cost of ________. Answer: $1700 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: Vogel's approximation method AACSB: Analytical thinking 9 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 49) According to the minimum cell cost method, the initial solution would give to cell BI a loading of ________. Answer: 25 units Diff: 2 Section Heading: Solution of the Transportation Model Keywords: minimum cell cost method AACSB: Analytical thinking 50) According to the minimum cell cost method, the initial solution would have a total transportation cost of ________. Answer: $1700 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: minimum cell cost method AACSB: Analytical thinking 51) In a transportation problem, items are allocated from sources to destinations at a: A) maximum cost. B) minimum cost. C) minimum profit. D) minimum revenue. Answer: B Diff: 1 Section Heading: The Transportation Model Keywords: transportation problem, objective function, cost minimization AACSB: Application of knowledge 52) The transportation method assumes that: A) the number of rows is equal to the number of columns. B) there must be at least 2 rows and at least 2 columns. C) both A and B D) the product of rows minus 1 and columns minus 1 should not be less than the number of completed cells. Answer: B Diff: 2 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge 10 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 53) The transportation method is a linear programming technique where linearity can be found in which of the following ways? A) The cost of goods shipped from any source to any destination is a linear function of quantity shipped. B) The total cost associated with a given plan is a linear function of shipping costs. C) Cell evaluations assume linear movements through the matrix. D) The cost of goods shipped from any source to any destination is a linear function of the cost per unit. Answer: A Diff: 3 Section Heading: The Transportation Model Keywords: transportation method, transportation model AACSB: Application of knowledge 54) Which of the following assumptions is not an assumption of the transportation model? A) Shipping costs per unit are constant. B) There is one transportation route between each source and destination. C) There is one transportation mode between each source and destination. D) Actual total supply and actual total demand must be equal. Answer: D Diff: 2 Section Heading: The Transportation Model Keywords: transportation method, transportation model assumptions AACSB: Application of knowledge 55) The problem that deals with the distribution of goods from several sources to several destinations is the: A) network problem. B) assignment problem. C) transportation problem. D) transshipment problem. Answer: C Diff: 1 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge 11 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 56) In the linear programming formulation of a transportation network: A) there is one variable for each arc. B) there is one constraint for each node. C) the sum of variables corresponding to arcs out of an origin node is constrained by the supply at that node. D) all of the above Answer: D Diff: 2 Section Heading: The Transportation Model Keywords: linear programming formulation of a transportation problem AACSB: Application of knowledge 57) Which of the following assumptions is not an assumption of the transportation model? A) Shipping costs are constant. B) There is only one transportation route between source and destination. C) There is only one transportation mode between source and destination. D) Actual supply and actual demand must be equal. Answer: D Diff: 2 Section Heading: The Transportation Model Keywords: transportation method, transportation model assumptions AACSB: Application of knowledge 58) The ________ problem deals with the distribution of goods from several sources to several destinations. A) network B) assignment C) transportation D) transshipment Answer: C Diff: 1 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge 59) In a transportation problem, items are allocated from sources to destinations at a ________ cost. A) maximum B) minimum C) high D) low Answer: B Diff: 1 Section Heading: The Transportation Model Keywords: transportation problem AACSB: Application of knowledge 12 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 60) The linear programming model for a transportation problem has constraints for: A) supply at each source. B) supply at each source and demand at each destination. C) demand at each destination. D) a feasible solution. Answer: B Diff: 2 Section Heading: The Transportation Model Keywords: linear programming formulation of a transportation problem AACSB: Application of knowledge 61) In a balanced transportation model where supply equals demand, all constraints are: A) inequalities. B) equalities. C) A and B D) none of the above Answer: B Diff: 2 Section Heading: The Transportation Model Keywords: balanced transportation model, transportation model formulation AACSB: Application of knowledge 62) The supply and demand values along the outside rim of a tableau are called: A) rim requirements. B) rim columns. C) rim rows. D) all of the above Answer: A Diff: 3 Section Heading: The Transportation Model Keywords: rim requirements AACSB: Application of knowledge 63) Which of the following are assumptions or requirements of the transportation problem? A) Minimum quantities must be shipped. B) Shipping costs per unit do not vary with the quantity shipped. C) There can only be one source. D) all of the above Answer: B Diff: 3 Section Heading: The Transportation Model Keywords: assumptions of the transportation problem AACSB: Application of knowledge 13 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Use the following table and the information to answer the questions below. In the following transportation matrix, all cells except 2C have been evaluated and show no improvement. Evaluate that cell. 64) What is the reduced cost if we decide to allocate to cell 2C? A) -2 B) -1 C) 0 D) +1 Answer: A Diff: 2 Section Heading: The Transportation Model Keywords: stepping stone method, reduced cost AACSB: Analytical thinking 65) How many units would be allocated to cell 2C? A) 10 B) 14 C) 6 D) 0 Answer: B Diff: 3 Section Heading: The Transportation Model Keywords: stepping stone method, reduced cost AACSB: Analytical thinking 66) Make the necessary allocation to cell 2C and determine the total transportation cost. A) 936 B) 928 C) 908 D) 852 Answer: C Diff: 3 Section Heading: The Transportation Model Keywords: stepping stone method AACSB: Analytical thinking 14 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 67) Which of the following are assumptions or requirements of transportation problems? Goods are the same from each source. There must be a single source. Minimum quantities must be shipped. Shipping costs per unit do not vary with the quantity shipped. A) I and III B) I, II, and IV C) I and IV D) II and III Answer: D Diff: 2 Section Heading: The Transportation Model Keywords: transportation problem, assumptions AACSB: Application of knowledge 68) Consider the following transportation tableau which shows the initial solution. Evaluate the cost of allocating units to cell DR. A) -5 B) -2 C) 0 D) 5 Answer: D Diff: 2 Section Heading: The Transportation Model Keywords: stepping stone method, reduced cost AACSB: Analytical thinking 15 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 69) Consider the following transportation tableau which shows the initial solution. Evaluate the cost of allocating units to cell CR. A) -12 B) -9 C) -6 D) -2 Answer: B Diff: 2 Section Heading: The Transportation Model Keywords: stepping stone method, reduced cost AACSB: Analytical thinking 70) An assignment problem is a special form of transportation problem where all supply and demand values equal: A) -1 or 1. B) -1. C) 0. D) 1. Answer: D Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: assignment problem AACSB: Application of knowledge 71) Assignments are made to locations with ________ in the opportunity cost table. A) -1 or 1 B) -1 C) 1 D) 0 Answer: D Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: assignment problem, assignment problem solution procedure AACSB: Application of knowledge 16 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 72) If the number of unique assignments is ________ the number of rows or columns, a line test must be used. A) more than B) less than C) higher than D) equal to Answer: B Diff: 1 Section Heading: Solution of the Assignment Problem Keywords: assignment problem, assignment problem solution procedure AACSB: Application of knowledge 73) A transportation table that has a cell evaluation of 0 means that: A) the table is optimal. B) an equivalent alternative solution exists. C) supply and demand are equal. D) the solution is not optimal. Answer: B Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: transportation table, transportation model solution procedure AACSB: Application of knowledge 74) A transportation table contains an optimal solution when all the empty cell evaluations are: A) positive or 0. B) negative or 0. C) positive. D) negative. Answer: A Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: transportation table, transportation model solution procedure AACSB: Application of knowledge 75) In an assignment problem: A) one agent can do parts of several tasks. B) one task can be done by only one agent. C) each agent is assigned to its own best task. D) all of the above Answer: B Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: assignment problem AACSB: Application of knowledge 17 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 76) The difference between the assignment and the transportation problem is that: A) each supply and demand value is 1 in the assignment problem. B) total supply must equal total demand in the transportation problem. C) the number of origins must equal the number of destinations in the transportation problem. D) all of the above Answer: A Diff: 2 Section Heading: Solution of the Assignment Problem Keywords: assignment and the transportation problems AACSB: Application of knowledge 77) A company that repairs and maintains HVAC systems for businesses wants to assign three service teams to three geographical zones, one team to each zone. Because of the familiarity with each team to the companies located in a zone, there are differences in the efficiencies of each team, reflected in the service costs. The matrix below shows the service costs (in thousands of dollars) for each team in each zone. Assign each team to a zone that minimizes cost. A) Assign T1 to zone A, T2 to zone B, and T3 to zone C. B) Assign T1 to zone A, T2 to zone C, and T3 to zone B. C) Assign T1 to zone B, T2 to zone A, and T3 to zone C. D) Assign T1 to zone B, T2 to zone C, and T3 to zone A. Answer: C Diff: 3 Section Heading: Solution of the Assignment Problem Keywords: assignment AACSB: Analytical thinking 18 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Consider the plight of Hepner Industries, who produces soccer balls in four plants of varying capacities and must ship to Thatcher and Bidness to satisfy the historically strong demand for these devices. 1 2 3 4 Demand Thatcher 5 6 5 8 350 Bidness 6 4 3 6 250 Supply 150 100 200 150 78) What is the objective function for Hepner Industries? Answer: Min 5x11 + 6x12 + 6x21 + 4x22 + 5x31 + 3x32 + 8x41 + 6x42 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem formulation, objective function AACSB: Analytical thinking 79) What are the supply-side constraints for Hepner Industries? Answer: x11 +x12 ≤ 150 x21 + x22 ≤ 100 x31 + x32 ≤ 200 x41 + x42 ≤ 150 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem formulation, supply-side constraints AACSB: Analytical thinking 80) What are the demand-side constraints? Answer: x11 + x21 + x31 + x41 = 350 x12 + x22 + x32 + x42 = 250 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem formulation, demand-side constraints AACSB: Analytical thinking 81) What is the initial entry for cell Thatcher2 for the northwest corner solution? Answer: 100 Diff: 1 Section Heading: Solution of the Transportation Model Keywords: transportation problem formulation, northwest corner AACSB: Analytical thinking 19 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 82) What is the rim requirement for Bidness? Answer: 250 Diff: 1 Section Heading: Solution of the Transportation Model Keywords: transportation problem formulation, rim requirement AACSB: Analytical thinking 83) What is the entire starting position and cost of the northwest corner rule for Hepner Industries? Answer: The starting position is shown in the table. The initial cost is $3050. Thatcher 150 100 100 Bidness Supply 150 100 200 150 1 2 3 100 4 150 Demand 350 250 Diff: 1 Section Heading: Solution of the Transportation Model Keywords: transportation problem formulation, northwest corner AACSB: Analytical thinking 84) Start Hepner Industries with a northwest corner solution to their transportation problem. What does the table look like after two iterations of the stepping stone method if you strive for maximum improvement with each step? Answer: The starting position is shown in the table. The initial cost is $3050. 1 2 3 4 Demand Thatcher 150 100 100 350 Bidness 100 150 250 Supply 150 100 200 150 It turns out that the northwest corner rule is optimal (actually there are multiple optimal solutions). The cost remains $3050. Thatcher 150 100 100 Bidness Supply 150 100 200 150 1 2 3 100 4 150 Demand 350 250 Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem formulation, northwest corner AACSB: Analytical thinking 20 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 85) Consider the following transportation tableau with the initial solution provided. Use the stepping stone method to identify a better allocation. Answer: Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation, stepping stone AACSB: Analytical thinking 21 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 86) An independent operator is planning shipments of gasoline from two sources to three destinations. Per ton transportation costs are given in the following table. There are 1000 tons available at A and 1300 tons available at B. Since the destinations want as much as possible, the owner has decided to ship out all available quantities. Solve using either stepping stone or MODI. Answer: 1300 tons will be sent to D and 1000 will be sent to C. None will be sent to E, since minimum demand requirements are not specified for each destination. Diff: 2 Section Heading: Solution of the Transportation Model Keywords: transportation problem AACSB: Analytical thinking 87) A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work; however, their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does which manuscript. Estimates of editing times (in hours) for each manuscript by each editor are: How many variables are involved in this assignment method? Answer: 25 Diff: 3 Section Heading: Solution of the Assignment Model Keywords: assignment model formulation AACSB: Analytical thinking 22 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 88) A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work; however, their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does which manuscript. Estimates of editing times (in hours) for each manuscript by each editor are: How many constraints are needed? Answer: 10 Diff: 3 Section Heading: Solution of the Assignment Model Keywords: assignment model formulation, constraints AACSB: Analytical thinking 23 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 89) The student internship director needs as much coverage as possible in the office next week. The more hours that can be put in each day, the better. She has asked the students to provide a list of how many hours they are available each day of the week. Each student can be there on only one day and there must be a student in the office each day of the week. Use the table below and the tables provided to determine the schedule that gives the most coverage. Note that the objective of this problem is to maximize the hours worked, not minimize. Student A B C D E Mon 2 3 6 7 4 Tue 4 2 8 4 5 Wed 8 7 6 3 3 Thurs 4 3 5 6 1 Fri 6 2 4 8 4 Answer: Convert to a minimization problem by subtracting each value from 8: Student Mon Tue Wed Thurs Fri A 6 4 0 4 2 B 5 6 1 5 6 C 2 0 2 3 4 D 1 4 5 2 0 E 4 3 5 7 4 2. Subtract the minimum value in each row from all other row values: Student Mon Tue Wed Thurs Fri A 6 4 0 4 2 B 4 5 0 4 5 C 2 0 2 3 4 D 1 4 5 2 0 E 1 0 2 4 1 3. Subtract the minimum column value in each column from all other column values: Student Mon Tue Wed Thurs Fri A 5 4 0 2 2 B 3 5 0 2 5 C 1 0 2 1 4 D 0 4 5 0 0 E 0 0 2 2 1 24 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 4. Conduct the line test: 5. Subtract the minimum value from all uncovered numbers and add it to the intersection: Student Mon Tue Wed Thurs Fri A 3 2 0 0 0 B 1 3 0 0 3 C 1 0 4 1 4 D 0 4 6 0 0 E 0 0 4 2 1 6. There are multiple optimal solutions: Solution Mon Tue Wed Thurs Fri 1 2 3 E E E C C C A B B B A D D D A Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Analytical thinking 25 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) Hours Covered 31 31 31 lOMoARcPSD|26927854 90) There are 4 jobs in a 4-person office that must be done as quickly as possible. The supervisor has used the assignment method to assign people to jobs, and has completed the first step. She had to rush off to a meeting and has asked to assign the jobs to the people before she returns. The original matrix which shows the expected completion time for each person for each job, and the one she just completed are both shown below. Job A B C D Ruth 8 13 38 19 Steve 26 28 19 26 Valerie 17 4 18 24 Wayne 11 26 15 10 Job A B C D Ruth 0 9 23 9 Steve 18 24 4 16 Valerie 9 0 3 14 Wayne 3 22 0 0 Which person should be assigned to which job? How long will the jobs take? Answer: Job Ruth Steve Valerie Wayne A 0 14 9 3 B 9 20 0 22 C 23 0 3 0 D 9 12 14 0 Ruth does job A. Valerie does job B. Steve does job C. Wayne does job D. Total time is 41 minutes. Diff: 2 Section Heading: Solution of the Assignment Model Keywords: assignment problem AACSB: Analytical thinking 26 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Introduction to Management Science, 13e, Global Edition (Taylor) Chapter 12 Decision Analysis 1) A state of nature is an actual event that may occur in the future. Answer: TRUE Diff: 1 Page Ref: 567 Section Heading: Components of Decision Making Keywords: state of nature AACSB: Application of knowledge 2) A payoff table is a means of organizing a decision situation, including the payoffs from different decisions given the various states of nature. Answer: TRUE Diff: 1 Page Ref: 567 Section Heading: Components of Decision Making Keywords: payoff table AACSB: Application of knowledge 3) The maximax criterion results in the maximum of the maximum payoffs. Answer: TRUE Diff: 2 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Application of knowledge 4) The maximin approach involves choosing the alternative with the highest payoff. Answer: FALSE Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Application of knowledge 5) Regret is the difference between the payoff from the best decision and all other decision payoffs. Answer: TRUE Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Application of knowledge 6) The minimax regret criterion minimizes the maximum regret. Answer: TRUE Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Application of knowledge 1 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 7) The minimax regret criterion maximizes the minimum regret. Answer: FALSE Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Application of knowledge 8) The Hurwicz criterion is a compromise between the maximax and maximin criteria. Answer: TRUE Diff: 2 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge 9) The Hurwicz criterion is a compromise between the minimax and minimin criteria. Answer: FALSE Diff: 2 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge 10) The coefficient of optimism is a measure of the decision maker's optimism. Answer: TRUE Diff: 1 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge 11) The Hurwicz criterion multiplies the best payoff by the coefficient of optimism. Answer: TRUE Diff: 1 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge 12) The Hurwicz criterion multiplies the worst payoff by the coefficient of optimism. Answer: FALSE Diff: 1 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge 2 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 13) A dominant decision is one that has a better payoff than another decision under each state of nature. Answer: TRUE Diff: 1 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: dominant decision AACSB: Application of knowledge 14) The appropriate criterion is dependent on the risk personality and philosophy of the decision maker. Answer: TRUE Diff: 3 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: decision making criteria AACSB: Application of knowledge 15) The maximax criterion is optimistic. Answer: TRUE Diff: 3 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: decision making criteria AACSB: Application of knowledge 16) The maximin criterion maximizes the minimum regret. Answer: FALSE Diff: 1 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Application of knowledge 17) The minimax criterion minimizes the maximum payoff. Answer: FALSE Diff: 1 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax criterion AACSB: Application of knowledge 18) Regret and opportunity loss mean the same thing. Answer: TRUE Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: expected value of perfect information AACSB: Application of knowledge 3 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 19) The equal likelihood criterion assigns a probability of 0.5 to each state of nature. Answer: FALSE Diff: 1 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Application of knowledge 20) Expected opportunity loss is the expected value of the regret for each decision. Answer: TRUE Diff: 2 Page Ref: 576 Section Heading: Decision Making with Probabilities Keywords: expected opportunity loss, minimax regret criterion AACSB: Application of knowledge 21) When using decision trees, branches with the greatest expected value are selected. Answer: TRUE Diff: 1 Page Ref: 581 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Application of knowledge 22) A decision tree is a diagram consisting of circular decision nodes, square probability nodes, and branches. Answer: FALSE Diff: 1 Page Ref: 581 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Application of knowledge 23) Additional information is used to alter the marginal probability of occurrence of an event in Bayesian analysis. Answer: TRUE Diff: 1 Page Ref: 590 Section Heading: Decision Analysis with Additional Information Keywords: Bayesian analysis AACSB: Application of knowledge 24) A conditional probability is the probability that two events will occur simultaneously. Answer: FALSE Diff: 1 Page Ref: 590 Section Heading: Decision Analysis with Additional Information Keywords: conditional probability AACSB: Application of knowledge 4 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 25) A posterior probability is the likelihood that an event has occurred after the decision maker has reached a decision. Answer: FALSE Diff: 1 Page Ref: 591 Section Heading: Decision Analysis with Additional Information Keywords: posterior (revised) probability AACSB: Application of knowledge 26) Events are mutually exclusive if one, and only one, can occur at a time. Answer: TRUE Diff: 1 Page Ref: 592 Section Heading: Decision Analysis with Additional Information Keywords: mutually exclusive events AACSB: Application of knowledge 27) The expected value of perfect information divided by the expected value of sample information is the efficiency of perfect information. Answer: FALSE Diff: 1 Page Ref: 596 Section Heading: Decision Analysis with Additional Information Keywords: efficiency of sample information AACSB: Analytical thinking 28) When the ________ criterion is used, the maximum of the maximum payoffs is selected. Answer: maximax Diff: 1 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: decision making without probabilities maximax criterion AACSB: Application of knowledge 29) When the ________ criterion is used, the maximum of the minimum payoffs is selected. Answer: maximin Diff: 1 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: decision making without probabilities, minimax criterion AACSB: Application of knowledge 30) ________ is the difference between the payoff from the best decision and all other decision payoffs. Answer: Regret Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: regret, minimax regret criterion AACSB: Application of knowledge 5 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 31) The ________ is a compromise between the maximax and the maximin criterion. Answer: Hurwicz criterion Diff: 2 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge 32) The ________ is a measure of the decision maker’s optimism. Answer: coefficient of optimism Diff: 2 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: coefficient of optimism AACSB: Application of knowledge 33) A(n) ________ decision is one that has a better payoff than another decision under each state of nature. Answer: dominant Diff: 2 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: dominant decision AACSB: Application of knowledge 34) A(n) ________ structures decisions with a series of nodes. Answer: decision tree Diff: 1 Page Ref: 579 Section Heading: Decision Making without Probabilities Keywords: decision trees AACSB: Application of knowledge 35) The ________ of sample information is the ratio of the expected value of sample information to the expected value of perfect information. Answer: efficiency Diff: 1 Page Ref: 596 Section Heading: Decision Analysis with Additional Information Keywords: expected value of sample information AACSB: Application of knowledge 36) When the ________ criterion is used, the decision maker selects the decision alternative that minimizes the maximum regret. Answer: minimax regret Diff: 1 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax criterion AACSB: Application of knowledge 6 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 37) A(n) ________ decision tree illustrates a situation requiring a series of decisions. Answer: sequential Diff: 1 Page Ref: 585 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Application of knowledge 38) ________ is a measure of personal satisfaction derived from money. Answer: Utility Diff: 1 Page Ref: 597 Section Heading: Utility Keywords: utility AACSB: Application of knowledge 39) People who forgo a high expected value to avoid a disaster with a low probability are ________. Answer: risk averters -or- risk averse Diff: 1 Page Ref: 597 Section Heading: Decision Making with Probabilities Keywords: risk averters, utility AACSB: Application of knowledge 40) The efficiency of sample information is the ratio of the expected value of sample information to ________. Answer: the expected value of perfect information Diff: 1 Page Ref: 596 Section Heading: Decision Analysis with Additional Information Keywords: expected value of perfect information AACSB: Analytical thinking 41) The difference in the expected value with additional information and without additional information is ________. Answer: the expected value of sample information Diff: 1 Page Ref: 595 Section Heading: Decision Analysis with Additional Information Keywords: expected value of sample information AACSB: Analytical thinking 42) The efficiency of sample information multiplied by the expected value of perfect information is ________. Answer: the expected value of sample information Diff: 1 Page Ref: 596 Section Heading: Decision Analysis with Additional Information Keywords: expected value of sample information AACSB: Analytical thinking 7 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 43) If only one of three events can occur at any given time, the events are ________. Answer: mutually exclusive Diff: 1 Page Ref: 592 Section Heading: Decision Analysis with Additional Information Keywords: mutually exclusive events AACSB: Application of knowledge 44) If the decision maker receives additional information such that the marginal probabilities of certain events should be modified, these revised probabilities are called ________. Answer: posterior probabilities Diff: 1 Page Ref: 591 Section Heading: Decision Analysis with Additional Information Keywords: posterior (revised) probability AACSB: Application of knowledge 45) The maximax criterion results in the: A) maximum of the minimum payoffs. B) maximum of the maximum payoffs. C) minimum of the maximum payoffs. D) minimum of the minimum payoffs. Answer: B Diff: 1 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Application of knowledge 46) The maximin criterion results in the: A) minimum of the maximum payoffs. B) maximum of the maximum payoffs. C) maximum of the minimum payoffs. D) minimum of the minimum payoffs. Answer: C Diff: 1 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Application of knowledge 47) Regret is the difference between the payoff from the: A) best decision and all other decision payoffs. B) worst decision and all other decision payoffs. C) best decision and the worst decision payoffs. D) none of the above Answer: A Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: regret, minimax regret criterion AACSB: Application of knowledge 8 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 48) The ________ minimizes the maximum regret. A) maximax regret criterion B) minimax regret criterion C) minimin regret criterion D) maximin regret criterion Answer: B Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Application of knowledge 49) The minimax regret criterion: A) maximizes the minimum regret. B) minimizes the minimum regret. C) minimizes the maximum regret. D) maximizes the maximum regret. Answer: C Diff: 1 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Application of knowledge 50) Determining the worst payoff for each alternative and choosing the alternative with the best worst is called: A) maximin. B) minimin. C) maximax. D) minimax. Answer: A Diff: 1 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Application of knowledge 51) The maximin approach to decision making refers to: A) minimizing the maximum return. B) maximizing the minimum return. C) maximizing the maximum return. D) minimizing the minimum return. Answer: B Diff: 1 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Application of knowledge 9 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 52) The term opportunity loss is most closely related to: A) maximin regret. B) maximax regret. C) minimax regret. D) minimin regret. Answer: C Diff: 2 Page Ref: 560 Section Heading: Decision Making without Probabilities Keywords: expected opportunity loss, minimax regret criterion AACSB: Application of knowledge 53) The Hurwicz criterion is a compromise: A) between the maximin and minimax criteria. B) between the minimax and maximax criteria. C) between the maximax and maximin criteria. D) none of the above Answer: C Diff: 2 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge 54) The Hurwicz criterion multiplies the: A) best payoff by the coefficient of optimism. B) worst payoff by the coefficient of optimism. C) best payoff by the worst payoff. D) none of the above Answer: A Diff: 1 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge 55) The basic decision environment categories are: A) certainty. B) risk. C) uncertainty. D) all of the above Answer: D Diff: 2 Page Ref: 567 Section Heading: Decision Making without Probabilities Keywords: decision making AACSB: Application of knowledge 10 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Napoleon is contemplating four institutions of higher learning as options for a Masters in Business Administration. Each university has strong and weak points and the demand for MBA graduates is uncertain. The availability of jobs, student loans, and financial support will have a significant impact on Napoleon's ultimate decision. Vanderbilt and Seattle University have comparatively high tuition, which would necessitate Napoleon take out student loans resulting in possibly substantial student loan debt. In a tight market, degrees with that cachet might spell the difference between a hefty paycheck and a piddling unemployment check. Northeastern State University and Texas Tech University hold the advantage of comparatively low tuition but a more regional appeal in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist with the decision. Together they forecast three possible scenarios for the job market and institutional success and predict annual cash flows associated with an MBA from each institution. All cash flows in the table are in thousands of dollars. School Vanderbilt Texas Tech Seattle Northeastern State Scenario 1 95 55 90 65 Scenario 2 20 60 10 50 Scenario 3 -10 60 80 60 56) Under which decision making criterion is Vanderbilt University the optimal choice? A) maximax B) maximin C) minimax regret D) equally likely Answer: A Diff: 2 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking 57) Under which decision making criterion is Texas Tech University the optimal decision? A) maximax B) maximin C) minimax regret D) equally likely Answer: B Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking 11 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 58) Under which criterion is Seattle University the optimal decision? A) maximax B) maximin C) minimax regret D) equally likely Answer: D Diff: 2 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking 59) Under which criterion is Northeastern State University the optimal decision? A) maximax B) maximin C) minimax regret D) equally likely Answer: C Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking 60) Suppose that the likelihood for each of the scenarios 1 through 3 is 0.3, 0.4, and 0.3, respectively. What is the optimal decision under the expected opportunity loss criterion? A) Vanderbilt University B) Texas Tech University C) Seattle University D) Northeastern State University Answer: B Diff: 2 Page Ref: 576 Section Heading: Decision Making with Probabilities Keywords: expected opportunity loss AACSB: Analytical thinking 12 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 The Vacation Final exams are almost here and once they are done, it will be time to reward myself with a welldeserved vacation. As a state employee, I haven't seen a raise since... well, ever. Thus an important criterion, in fact the most important criterion is to find an exotic region that can be visited inexpensively. There are three states of nature that could impact costs in these five areas of interest, and they correspond to the relative strength of the US Dollar against that region's dominant currency. Rather than squander my time doing any actual publishable research, instead I have determined the average cost per day to visit each region under each of the possible states of nature. This table, which should not be construed as actual vacation advice, appears below. Region Eastern Europe Southeast Asia Australia Galapagos Islands Scandinavia Strong Dollar 33 41 45 37 38 Middling Dollar 54 56 44 35 11 Weak Dollar 57 36 58 26 48 61) An optimistic vacationer would opt for: A) Scandinavia. B) Galapagos Islands. C) Australia. D) Eastern Europe. Answer: A Diff: 2 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: minimin criterion AACSB: Analytical thinking 62) An pessimistic vacationer would opt for: A) Scandinavia. B) Galapagos Islands. C) Australia. D) Eastern Europe. Answer: B Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax criterion AACSB: Analytical thinking 13 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 63) After staring blankly at the options for several hours, the family decides they truly have no idea which value of the dollar would be more likely and overall feel neither optimistic nor pessimistic. What's the safest choice for them to make? A) Scandinavia B) Australia C) Galapagos Islands D) Eastern Europe Answer: C Diff: 2 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking 64) What do the regrets look like for Scandinavia from left to right? A) 0, 21, 24 B) 0, 15, 5 C) 6, 0, 16 D) 5, 0, 12 Answer: D Diff: 2 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: minimax criterion, regret table AACSB: Analytical thinking 65) What is the vacation of choice under the minimax regret criterion? A) Galapagos Islands B) Eastern Europe C) Southeast Asia D) Australia Answer: A Diff: 2 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: minimax criterion, regret table AACSB: Analytical thinking 66) What does the coefficient of optimism need to exceed in order for the Galapagos Islands to not be the vacation destination of choice? A) 0.80 B) 0.77 C) 0.74 D) 0.71 Answer: B Diff: 3 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking 14 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Cold & Calculating The cold, calculating father did exactly that when examining the 27-year-old failure to launch man child that had turned his walk in closet into a bedroom. As he saw it, there were five alternatives; each had its advantages and disadvantages, and under different circumstances, each had a different financial incentive. He laid it all out neatly in a table, but as not to arouse suspicion, he left the table's labels very generic, so the alternatives were simply labeled A through E while the different circumstances were simply numbered one through three. He flicked the gray ash off of his favorite purple smoking jacket and pondered the best course of action under each possible future. It was good to be devious, he decided. A B C D E One 19 26 24 43 36 Two 6 5 18 34 34 Three 20 48 17 15 15 67) It was tough to be optimistic, but the cold, calculating father did exactly that, inspired by a particularly smooth single malt scotch. Which alternative would be the best choice given this rare state of optimism? A) A B) B C) C D) D Answer: B Diff: 2 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking 68) The father had built his fortune as a real estate speculator and now devoted his energies to his new passion, pessimism. Which alternative would be the best choice given this new hobby? A) A B) B C) C D) D Answer: C Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking 15 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 69) "Regrets? I've had a few," and his voice trailed off. He was speaking to no one in particular, which he found himself doing with alarming frequency. If at all possible, he made decisions that would allow him to look back with as little regret as possible. Which alternative would be the best choice given this proclivity for minimizing regret? A) A B) B C) C D) D Answer: A Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking 70) He set the analysis aside for a few days and when he noticed it on his drawing table he studied it. He vaguely remembered the potential courses of action but couldn't for the life of himself remember what the different states of nature were. "This is certainly embarrassing," he muttered. Perhaps it didn't really matter as long as he treated each state of nature as equally likely. They certainly were in his own mind now that he couldn't remember what they were. "If that's not the definition of equally likely, I don't know what is," he commented to his faithful manservant Jeeves. Which alternative would be the best choice given this predicament? A) A B) B C) C D) D Answer: D Diff: 2 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking 71) He set the analysis aside for a few days and had forgotten about it completely until one night when his frequent dining companion Leonid Hurwicz visited his house and retired to the drawing room for an aperitif. "What you must do, my friend," Hurwicz began, "is to declare your coefficient of optimism, which can be tricky." After forty-five minutes of intense concentration, the cold, calculating father decided that his coefficient of optimism was 0.5. What is the optimal choice for him? A) A B) B C) C D) D Answer: D Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking 16 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 72) He set the analysis aside for a few days and had forgotten about it completely until one night when his frequent dining companion Leonid Hurwicz visited his house and retired to the drawing room for an aperitif. "What you must do, my friend," Hurwicz began, "is to declare your coefficient of optimism, which can be tricky." After forty-five minutes of intense concentration, the cold, calculating father decided that his coefficient of optimism was 0.7. What is the optimal choice for him? A) A B) B C) C D) D Answer: B Diff: 2 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking 73) He set the analysis aside for a few days and had forgotten about it completely until one night when his frequent dining companion Leonid Hurwicz visited his house and retired to the drawing room for an aperitif. "What you must do, my friend," Hurwicz began, "is to declare your coefficient of optimism, which can be tricky." After forty-five minutes of intense concentration, the cold, calculating father decided that his coefficient of optimism was 0.5. "Wait a minute Hurwicz, that figure sounds as if I'm afraid of making a decision," the father intoned. "It seems that depending on how optimistic I am, the optimal choice changes between alternative B and alternative D." What coefficient of optimism would make the cold, calculating father indifferent between these two alternatives? A) 0.583 B) 0.616 C) 0.666 D) 0.714 Answer: C Diff: 2 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking 17 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 74) He set the analysis aside for a few days and had forgotten about it completely until one night when his frequent dining companion Leonid Hurwicz visited his house and retired to the drawing room for an aperitif. "What you must do, my friend," Hurwicz began, "is to declare your coefficient of optimism, which can be tricky." After forty-five minutes of intense concentration, the cold, calculating father decided that his coefficient of optimism was 0.5. "Wait a minute Hurwicz, that figure sounds as if I'm afraid of making a decision," the father intoned. "It seems that depending on how optimistic I am, the optimal choice changes between alternative C and alternative D." What coefficient of optimism would make the cold, calculating father indifferent between these two alternatives? A) 0.096 B) 0.125 C) 0.167 D) 0.183 Answer: A Diff: 2 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking 75) The basic decision environment categories are: A) certainty and risk. B) risk and uncertainty. C) certainty and uncertainty. D) certainty, uncertainty and risk. Answer: D Diff: 2 Page Ref: 567 Section Heading: Decision Making without Probabilities Keywords: decision making AACSB: Application of knowledge 76) The Hurwicz criterion: A) multiplies the worst payoff by one minus the coefficient of optimism. B) multiplies the best payoff by one minus the coefficient of optimism. C) is a compromise between the minimax and maximin criteria. D) all of the above Answer: A Diff: 1 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Application of knowledge 18 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 77) The appropriate criterion is dependent on: A) the risk personality of the decision maker. B) the number of nodes in the decision tree. C) the magnitude of the payoffs. D) none of the above Answer: A Diff: 3 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: decision making AACSB: Application of knowledge 78) The ________ is a measure of the decision maker's optimism. A) equal likelihood criterion B) dominant decision C) coefficient of optimism D) opportunity loss Answer: C Diff: 2 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: coefficient of optimism, Hurwicz criterion AACSB: Application of knowledge 79) The ________ multiplies the decision payoff for each state of nature by an equal weight. A) dominant decision B) coefficient of optimism C) equal likelihood criterion D) none of the above Answer: C Diff: 2 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Application of knowledge 80) A(n) ________ is one that has a better payoff than another decision under each state of nature. A) coefficient of optimism B) equal likelihood criterion C) dominant decision D) none of the above Answer: C Diff: 2 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: dominant decision AACSB: Application of knowledge 19 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow. 81) The maximax strategy is: A) Buy. B) Rent. C) Lease. D) Brisk. Answer: A Diff: 1 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking 82) The maximin strategy is: A) Buy. B) Rent. C) Lease. D) Brisk. Answer: C Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking 83) The equal likelihood criterion strategy is: A) Buy. B) Rent. C) Lease. D) Brisk. Answer: C Diff: 2 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking 20 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 84) If the probability of brisk business is .40 and for slow business is .60, the expected value of perfect information is: A) 12. B) 55. C) 57. D) 69. Answer: A Diff: 2 Page Ref: 578 Section Heading: Decision Making without Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking 85) The ________ is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence. A) expected value B) expected value of perfect information C) expected opportunity loss D) none of the above Answer: A Diff: 2 Page Ref: 575 Section Heading: Decision Making with Probabilities Keywords: expected value AACSB: Application of knowledge 86) The ________ is the expected value of the regret for each decision. A) expected value B) expected opportunity loss C) expected value of perfect information D) none of the above Answer: B Diff: 2 Page Ref: 576 Section Heading: Decision Making with Probabilities Keywords: expected opportunity loss AACSB: Application of knowledge 87) A tabular presentation that shows the outcome for each decision alternative under the various possible states of nature is called a: A) decision tree. B) payoff table. C) feasible region. D) payback matrix. Answer: B Diff: 2 Page Ref: 567 Section Heading: Components of Decision Making Keywords: payoff table AACSB: Application of knowledge 21 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 88) The ________ is the maximum amount a decision maker would pay for additional information. A) expected opportunity loss B) expected value C) expected value of perfect information D) bid price Answer: C Diff: 2 Page Ref: 578 Section Heading: Decision Making with Probabilities Keywords: expected value of perfect information AACSB: Application of knowledge 89) A decision tree is a diagram consisting of: A) branch angles that vary as likelihoods increase. B) triangle probability nodes. C) branches representing decision alternatives. D) perfect information. Answer: C Diff: 1 Page Ref: 569 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Application of knowledge 90) In ________ additional information is used to alter the marginal probability of the occurrence of an event. A) Bayesian analysis B) decision analysis C) probability analysis D) decision making under certainty Answer: A Diff: 2 Page Ref: 590 Section Heading: Decision Analysis with Additional Information Keywords: Bayesian analysis AACSB: Application of knowledge 91) A ________ probability is the probability that an event will occur given that another event has already occurred. A) posterior B) conditional C) marginal D) low Answer: B Diff: 2 Page Ref: 590 Section Heading: Decision Analysis with Additional Information Keywords: conditional AACSB: Application of knowledge 22 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 92) A ________ probability is the altered marginal probability of an event based on additional information. A) marginal B) conditional C) posterior D) none of the above Answer: C Diff: 2 Page Ref: 591 Section Heading: Decision Analysis with Additional Information Keywords: posterior AACSB: Application of knowledge 93) The efficiency of sample information is the ratio of the expected value of sample information to the: A) expected value of perfect information. B) expected value. C) utilization rate. D) coefficient of optimism. Answer: A Diff: 2 Page Ref: 596 Section Heading: Decision Analysis with Additional Information Keywords: efficiency of sample information AACSB: Application of knowledge 94) The expected value of sample information: A) is never more than EVPI. B) can be greater or less than EVPI. C) can be positive or negative. D) is equivalent to the EVPI. Answer: A Diff: 2 Page Ref: 595 Section Heading: Utility Keywords: efficiency of sample information AACSB: Application of knowledge 95) People who forgo a high expected value to avoid a disaster with a low probability are: A) risk takers. B) risk averters. C) risk calculators. D) risk predictors. Answer: B Diff: 1 Page Ref: 597 Section Heading: Utility Keywords: risk averters, utility AACSB: Application of knowledge 23 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 96) People who take a chance on a bonanza with a very low probability of occurrence in lieu of a sure thing are: A) risk takers. B) risk averters. C) risk calculators. D) risk predictors. Answer: A Diff: 1 Page Ref: 597 Section Heading: Utility Keywords: risk takers, utility AACSB: Application of knowledge 97) Utiles are units of ________ measures of utility. A) quantitative B) objective C) subjective D) qualitative Answer: C Diff: 3 Page Ref: 587 Section Heading: Utility Keywords: utility AACSB: Application of knowledge A small entrepreneurial company is trying to decide between developing two different products that they believe they can sell to two potential companies, one large and one small. If they develop Product A, they have a 50% chance of selling it to the large company with annual purchases of about 20,000 units. If the large company won't purchase it, then they think they have an 80% chance of placing it with a smaller company, with sales of 15,000 units. On the other hand, if they develop Product B, they feel they have a 40% chance of selling it to the large company, resulting in annual sales of about 17,000 units. If the large company doesn't buy it, they have a 50% chance of selling it to the small company with sales of 20,000 units. 98) What is the probability that Product A will being purchased by the smaller company? A) 0.8 B) 0.5 C) 0.4 D) 0.2 Answer: C Diff: 2 Page Ref: 581 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Analytical thinking 24 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 99) What is the probability that Product B will being purchased by the smaller company? A) 0.8 B) 0.5 C) 0.4 D) 0.3 Answer: D Diff: 2 Page Ref: 579 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Analytical thinking 100) How many units of Product A can they expect to sell? A) 20,000 B) 17,000 C) 16,000 D) 15,000 Answer: C Diff: 2 Page Ref: 579 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Analytical thinking John Connor and his friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of death and dismemberment for each activity under the various possibilities for sentient cybernetic organisms they may encounter. They have no idea which of the terminators, the T-X, the T-1000, or the T-100, they might encounter on their outing. T-X T-1000 T-100 Picnic 100 150 200 Rappelling 150 125 50 Disable Skynet 75 100 125 101) If the group is optimistic, what decision should they make? Answer: They should disable Skynet due to its 50 unit cost Diff: 3 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking 102) If the group is conservative, what decision will they make? Answer: They should go on a picnic and enjoy the 150 cost. Diff: 3 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking 25 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 103) If the group chooses to minimize their maximum regret, what activity will they choose? Answer: Rappelling is the clear choice with its 75 unit cost Diff: 3 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking 104) If the probabilities of the T-X, T-1000, and T-100 are 0.2, 0.4, and 0.4, respectively, then what decision should be made using the expected value criterion? Answer: Going on a picnic and enjoying an expected loss of 110 units is optimal Diff: 3 Page Ref: 575 Section Heading: Decision Making with Probabilities Keywords: expected value criterion AACSB: Analytical thinking 105) If the probabilities of the T-X, T-1000, and T-100 are 0.2, 0.4, and 0.4, respectively, then what is the EVPI for this situation? Answer: EVPI = 110 - 75 = 35 Diff: 3 Page Ref: 578 Section Heading: Decision Making without Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking Patrick Bateman is considering four alternatives Friday night. The payoff for each opportunity will depend on economic and other conditions, and are represented in the payoff table below. Return videotapes Dinner at Dorsia Pick up friends in his limo Design new business cards Poor 50 80 100 25 Average 25 300 15 75 Good 40 20 25 -50 Excellent 25 10 50 30 106) What decision would be made under maximax? Answer: Compare 75, 80, 300, and 25. Choose Dinner at Dorsia. Diff: 3 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking 107) What decision would be made under maximin? Answer: Compare 20, 15, -100, and 25. Choose Return videotapes. Diff: 3 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking 26 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 108) What decision would be made under minimax regret? Answer: Compare 225, 285, 40, and 275. Select Dinner at Dorsia. Diff: 3 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking 109) If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what investment would be made using the expected value criterion? Answer: Dinner at Dorsia with an EMV of 77.5. Diff: 3 Page Ref: 575 Section Heading: Decision Making without Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking 110) If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what is the expected value of perfect information? Answer: The EVPI is 19. Diff: 3 Page Ref: 578 Section Heading: Decision Making without Probabilities Keywords: expected value criterion AACSB: Analytical thinking 111) What set of probabilities for Poor through Excellent will result in a maximum EMV for returning videotapes that exceeds that for dinner at Dorsia if the smallest probability that can be assigned to any state of nature is 0.2? Answer: No set of probabilities can be chosen that make returning videotapes more rewarding than dinner at Dorsia given the 0.2 lower bound on likelihood. Even at 0.2, the value for the Average state of nature is 55 higher for Dorsia than returning videotapes. Diff: 3 Page Ref: 575 Section Heading: Decision Making without Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking 27 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 A professor has developed a payoff table that indicates the payoffs associated with a set of alternatives under two possible states of nature. Teach at another university Apply for the dean's job Go into industry Tenure $120,000 $40,000 $30,000 Fired $20,000 $180,000 $250,000 112) If the manager uses maximin as the decision criterion, which of the alternatives should she choose? Answer: maximin: Dean's job $40,000 Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking 113) If the manager uses maximax as the decision criterion, which of the alternatives should she choose? Answer: maximax: Industry position at $250,000 Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking 114) If the manager uses minimax regret as the decision criterion, which of the alternatives would she choose? Answer: Select Dean's job at $80,000 regret Diff: 2 Page Ref: 560 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking 115) Use the expected value criterion to select the best alternative. Assume that the probability of being fired is equal to 0.4. Answer: EV (Teach) = $80,000 EV (Dean) = $96,000 EV (Work) = $118,000 Select Go Into Industry as the optimal alternative. Here's a little-known fact: Going into industry is known as working. Functioning as the dean is known as deaning and it remains one of the biggest mistakes of my life... Diff: 2 Page Ref: 575 Section Heading: Decision Making without Probabilities Keywords: expected value criterion AACSB: Analytical thinking 28 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 116) Compute the expected value of perfect information assuming that the probability of being fired is equal to 0.4. Answer: EVPI = $54,000 Diff: 2 Page Ref: 578 Section Heading: Decision Making without Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues (in thousands) will vary with how well taxpayers comply with the new tax code. 117) If he uses the maximin criterion, how many new workers will he hire? Answer: 1 Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking 118) If he uses the minimax regret criterion, how many new workers will he hire? Answer: 2 Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking 119) If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%, respectively, what are the expected net revenues for the number of workers he will decide to hire? Answer: $50,000 Diff: 2 Page Ref: 576 Section Heading: Decision Making with Probabilities Keywords: expected value criterion AACSB: Analytical thinking 29 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 120) If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%, respectively, what is the expected value of perfect information? Answer: $26,000 Diff: 2 Page Ref: 578 Section Heading: Decision Making with Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either low or high, with probabilities estimated to be 0.4 and 0.6, respectively. If a small plant is built, and demand is high, the production manager may choose to maintain the current size or to expand. The net present value of profits is $223,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 50% chance that the net present value of the returns will be 330,000 and a 50% chance the estimated net present value of profits will be $210,000. If a small facility is built and demand is low, there is no reason to expand and the net present value of the profits is $200,000. However, if a large facility is built and the demand turns out to be low, the choice is to do nothing with a net present value of $40,000 or to stimulate demand through local advertising. The response to advertising can be either modest with a probability of .3 or favorable with a probability of .7. If the response to advertising is modest, the net present value of the profits is $20,000. However, if the response to advertising is favorable, then the net present value of the profits is $220,000. Finally, if the large plant is built and the demand happens to be high, the net present value of the profits $800,000. 121) Draw a decision tree. Answer: Diff: 2 Page Ref: 585 Section Heading: Decision Making with Probabilities Keywords: sequential decision tree AACSB: Analytical thinking 30 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 122) Draw a decision tree and determine the payoff for each decision and event node. Which alternative should the manufacturer choose? Answer: EV1 = (.3)(20,000) + (.7)((220,000) = $160,000 EV2 = (.5)(330,000) + (.5)((210,000) = $270,000 EV3 = (.4)(200,000) + (.6)((270,000) = $242,000 EV4 = (.4)(160,000) + (.6)((800,000) = $544,000 Since 544,000 > 242,000, build a large plant. Diff: 3 Page Ref: 585 Section Heading: Decision Making with Probabilities Keywords: sequential decision tree AACSB: Analytical thinking 31 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 123) If a student attends every management science class, the probability of passing the course is 0.80; but if the student only attends randomly, then the probability of passing the course is 0.50. If a student fails, he or she can take a makeup exam where the probability of passing is 0.60 if the student has attended every class. This probability of passing the makeup exam drops to 0.10 if the student has attended at random. Passing the course is worth 5 credits. Full time attendance "costs" 3 credits in terms of energy and time, whereas random attendance "costs" only 1 credit. Use a decision tree to decide which is the best attendance pattern to adopt. Assume that all failing students take the makeup exam and that the payoff for failing is equal to 0. Answer: The expected value of attending all classes is 4.6 - 3 = 1.6. The expected value of attending randomly is 2.75 - 1 = 1.75, so the student should attend at random. Diff: 2 Page Ref: 569 Section Heading: Decision Making with Probabilities Keywords: decision trees AACSB: Analytical thinking 32 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 The quality control manager for ENTA Inc. must decide whether to accept (A1), further analyze (A2), or reject (A3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (S1), 50 % chance that the lot is fair quality (S2), and 20% chance that the lot is good quality (S3). A1 A2 A3 S1 20 60 80 S2 30 70 50 S3 90 10 40 124) What action would you choose according to maximax criterion? Answer: (90 > 80 > 70), accept the lot, A1. Diff: 2 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking 125) What action would you choose according to maximin criterion? Answer: (10 < 20 < 40), reject the lot, A3. Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking 126) Construct the regret table. Answer: Regret Table S1 S2 S3 A1 60 40 0 A2 20 0 80 A3 0 20 50 Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax criterion, regret table AACSB: Analytical thinking 33 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 127) What action would you choose according to minimax regret criterion? Answer: Regret Table S1 S2 S3 A1 60 40 0 A2 20 0 80 A3 0 20 50 (80 > 60 > 50), therefore, reject the lot. Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax criterion AACSB: Analytical thinking 128) What action would you choose according to expected value criterion? Answer: EV1 = (.3)(20) + (.5)(30) + (.2)(90) = 39 EV2 = (.3)(60) + (.5)(70) + (.2)(10) = 55 EV3 = (.3)(80) + (.5)(50) + (.2)(40) = 57 Since 57 > 55 > 39, reject the lot. Diff: 2 Page Ref: 576 Section Heading: Decision Making with Probabilities Keywords: expected value criterion AACSB: Analytical thinking 129) What is the maximum amount that you would be willing to pay for perfect information? Answer: Expected payoff with perfect information = (.3)(80) + (.5)(70) + (.2)(90) = 77 EVPI = 77 - max (EV) = 77 -57 = 20 Diff: 3 Page Ref: 578 Section Heading: Decision Making with Probabilities Keywords: expected value of perfect information AACSB: Analytical thinking 130) Lucky Lucy is playing the slots in Reno, Nevada, holding her last silver dollar. There are three possible payoffs if she wins: one cherry, $1; two cherries, $5; or three cherries, $50. Anything else on the slot machine loses. Construct the payoff table for Lucky Lucy. Answer: Diff: 2 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: payoff table AACSB: Analytical thinking 34 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Cold & Calculating The cold, calculating father did exactly that when examining the 27-year-old failure to launch man child that had turned his walk in closet into a bedroom. As he saw it, there were five alternatives; each had its advantages and disadvantages, and under different circumstances, each had a different financial incentive. He laid it all out neatly in a table, but as not to arouse suspicion, he left the table's labels very generic, so the alternatives were simply labeled A through E while the different circumstances were simply numbered one through three. He flicked the gray ash off of his favorite purple smoking jacket and pondered the best course of action under each possible future. It was good to be devious, he decided. A B C D E One 19 26 24 43 36 Two 6 5 18 34 34 Three 20 48 17 15 15 He set the analysis aside for a few days and had forgotten about it completely until one night when his frequent dining companion Leonid Hurwicz visited his house and retired to the drawing room for an aperitif. "What you must do, my friend," Hurwicz began, "is to declare your coefficient of optimism, which can be tricky." After forty-five minutes of intense concentration, the cold, calculating father decided that his coefficient of optimism was 0.5. "Wait a minute Hurwicz, that figure sounds as if I'm afraid of making a decision," the father intoned. "It seems that depending on how optimistic I am, the optimal choice changes between alternative B and alternative D. Furthermore, another transition point exists between alternatives C and D. What is this devilry, Hurwicz?" 131) Help Leonid Hurwicz identify the range of coefficients of optimism that render alternatives, B, C, and D superior to all others. Answer: A coefficient of optimism from 0 up to 0.096 would make alternative C most attractive. A coefficient of optimism from 0.096 up to 0.666 would make alternative D most attractive. A coefficient of optimism beyond 0.666 would make alternative B most attractive. Diff: 3 Page Ref: 571 Section Heading: Decision Making without Probabilities Keywords: Hurwicz criterion AACSB: Analytical thinking 35 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 132) The cold, calculating father had little reason for optimism and tended towards a pessimistic view of the entire world. Still, it might be useful to see what the other half thinks, he thought to himself. Identify the optimal alternatives under these two opposite views of the world. Answer: The optimistic view of the world would suggest alternative B by virtue of its score of 48 in state of nature 3. The pessimistic view of things would select alternative C thanks to its lusty 17 under alternative 3. Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking 133) "Cletus, my boy," he said to his dog that was dozing peacefully before the fireplace, "I don't like to look back on my decisions with any regret. In fact, in my golden years I make most of my decisions so that when I do look back, I have as little regret as possible." What is the regret table and optimal choice given this state of mind? Answer: The regret table looks something like this: A B C D E 1 24 17 19 0 7 2 28 29 16 0 0 3 28 0 31 33 33 The minimum of the maximum regrets is the 28 associated with alternative A in state of nature 3. Diff: 3 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking 36 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Napoleon is contemplating four institutions of higher learning as options for a Masters in Business Administration. Each university has strong and weak points and the demand for MBA graduates is uncertain. The availability of jobs, student loans, and financial support will have a significant impact on Napoleon's ultimate decision. Vanderbilt and Seattle University have comparatively high tuition, which would necessitate Napoleon take out student loans resulting in possibly substantial student loan debt. In a tight market, degrees with that cachet might spell the difference between a hefty paycheck and a piddling unemployment check. Northeastern State University and Texas Tech University hold the advantage of comparatively low tuition but a more regional appeal in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist with the decision. Together they forecast three possible scenarios for the job market and institutional success and predict annual cash flows associated with an MBA from each institution. All cash flows in the table are in thousands of dollars. School Vanderbilt Texas Tech Seattle Northeastern State Scenario 1 95 55 90 65 Scenario 2 20 60 10 50 Scenario 3 -10 60 80 60 134) Kip tends to be extremely optimistic. Which decision making criterion would he naturally select and what conclusion would he recommend to Napoleon? Why? Answer: Maximax is the optimistic criterion, which would result in the selection of Vanderbilt as it has the best of the best payoffs among all alternatives. Diff: 2 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: maximax criterion AACSB: Analytical thinking 135) Pedro is extremely pessimistic. Which decision making criterion would he naturally select and what conclusion would he recommend to Napoleon? Why? Answer: Maximin is the pessimist's criterion. This would result in the selection of Texas Tech University by virtue of its $55,000 payoff being higher than all other alternatives' worst outcomes. Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: maximin criterion AACSB: Analytical thinking 136) Napoleon doesn't know what to think, since he has no idea which scenario will happen. Which criterion is he well-suited for and what is his decision? Answer: Napoleon is an equally-likely decision maker in this example, so he would opt for Seattle University and its $60,000 per year average. Diff: 2 Page Ref: 572 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking 37 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 137) Summer bursts into the meeting and announces that there's another way to consider the issue. Since Napoleon will have to live with his choice for the rest of his life, he might consider selecting the alternative that will cause him the least pain in hindsight when he compares his outcome with what he might have gained. Which criterion is she talking about, what is the best school for this criterion, and why? Answer: This is the minimax regret criterion. Northeastern State University is the MBA of choice under this criterion with a maximum regret of only $30,000 per year. Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking 138) Napoleon's Uncle Rico believes that the scenarios are not necessarily equally likely, and suggests that the likelihood of occurrence of Scenario 2 is 0.4 and the likelihood of occurrence of Scenarios 1 and 3 are both 0.3. What two criteria are most appropriate and what is the resulting decision? Answer: The two criteria are expected monetary value and expected opportunity loss. The EMV is highest for Texas Tech University at $58,500 and the EOL is the lowest for Texas Tech University at $18,000. Diff: 2 Page Ref: 576 Section Heading: Decision Making with Probabilities Keywords: expected opportunity loss AACSB: Analytical thinking 38 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 The Vacation Final exams are almost here and once they are done, it will be time to reward myself with a welldeserved vacation. As a state employee, I haven't seen a raise since... well, ever. Thus an important criterion, in fact the most important criterion is to find an exotic region that can be visited inexpensively. There are three states of nature that could impact costs in these five areas of interest, and they correspond to the relative strength of the US Dollar against that region's dominant currency. Rather than squander my time doing any actual publishable research, instead I have determined the average cost per day to visit each region under each of the possible states of nature. This table, which should not be construed as actual vacation advice, appears below. Region Eastern Europe Southeast Asia Australia Galapagos Islands Scandinavia Strong Dollar Middling Dollar Weak Dollar 33 54 57 41 56 36 45 44 58 37 35 26 38 11 48 139) My wife always looks on the bright side of life. Where would she recommend we travel and why? Answer: Maximax is the optimistic criterion when we consider profits, but these are costs, so an optimist would adopt the minimin criterion as most appropriate. The lowest of the lowest costs is $32 per day associated with Scandinavia. Hei suomi! Diff: 2 Page Ref: 569 Section Heading: Decision Making without Probabilities Keywords: minimin criterion AACSB: Analytical thinking 140) I'm a pessimistic person, perhaps it has to do with the twenty years in my chosen profession. Where should I recommend we travel and why? Answer: Maximin is the pessimistic criterion when we consider profits, but these are costs, so an pessimist would adopt the minimax criterion as most appropriate. The lowest of the highest costs is $38 per day associated with the Galapagos Islands. Hola Galapagos! Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimin criterion AACSB: Analytical thinking 141) I spend a lot of time second guessing myself and would hate to look back in a year or two and realize that I had spent more than I needed to. Where should I recommend we travel and why? Answer: This mindset screams for a minimax regret criterion. The lowest of the location regrets is the $4 associated with the Galapagos Islands. Hola Galapagos! Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking 39 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 142) I spend a lot of time second guessing myself and would hate to look back in a year or two and realize that I had spent more than I needed to. What does the regret table look like for this decision and what is the location of choice? Answer: This mindset screams for a minimax regret criterion. The regret table is: Eastern Europe Southeast Asia Australia Galapagos Scandinavia Strong $ 0 8 12 4 5 Middling $ 22 24 12 3 0 Weak $ 21 0 22 2 12 The lowest of the location maximum regrets is the $4 associated with the Galapagos Islands. Hola Galapagos! Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: minimax regret criterion AACSB: Analytical thinking 143) I have absolutely no clue what will happen with the strength of the dollar and can't imagine assigning likelihoods or adopting an optimistic or pessimistic stance. What's the safest bet for a destination and why? Answer: This mindset screams for an equally likely criterion. The lowest of the location averages is the $36.66 associated with the Galapagos Islands. Hola Galapagos! Diff: 2 Page Ref: 570 Section Heading: Decision Making without Probabilities Keywords: equal likelihood criterion AACSB: Analytical thinking 40 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Consider the following decision tree. 144) What is the expected value at node 4? Answer: $600 Diff: 1 Page Ref: 585 Section Heading: Decision Making with Probabilities Keywords: expected value, decision trees AACSB: Analytical thinking 145) What is the value associated with node 3? Answer: $2,500 Diff: 2 Page Ref: 585 Section Heading: Decision Making without Probabilities Keywords: expected value, decision trees AACSB: Analytical thinking 146) Which decision, A or B, is best? What is the expected value of this decision? Answer: A, expected payoff = $2,100 Diff: 2 Page Ref: 586 Section Heading: Decision Making with Probabilities Keywords: expected value, decision trees AACSB: Analytical thinking 41 Copyright © 2019 Pearson Education Ltd. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 1 Chapter 7 Linear Programming Models: Test 3 Bank with Answers 1) Management resources that need control include machinery usage, labor volume, money spent, time used, warehouse space used, and material usage. Answer: TRUE 2) Any linear programming problem can be solved using the graphical solution procedure. Answer: FALSE 3) There are no limitations on the number of constraints or variables that can be graphed to solve an LP problem. Answer: FALSE 4) Resource restrictions are called constraints. Answer: TRUE 5) The set of solution points that satisfies all of a linear programming problem's constraints simultaneously is defined as the feasible region in graphical linear programming. Answer: TRUE 6) An objective function is necessary in a maximization problem but is not required in a minimization problem. Answer: FALSE 7) In some instances, an infeasible solution may be the optimum found by the corner point method. Answer: FALSE 8) The solution to a linear programming problem must always lie on a constraint. Answer: TRUE 9) In a linear program, the constraints must be linear, but the objective function may be nonlinear. Answer: FALSE 10) The term slack is associated with ≥ constraints. Answer: FALSE 11) The term surplus is associated with ≥ constraints. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 2 Answer: TRUE 12) Sensitivity analysis enables us to look at the effects of changing the coefficients in the objective function, one at a time. Answer: TRUE 13) A widely used mathematical programming technique designed to help managers and decision making relative to resource allocation is called A) linear programming. B) computer programming. C) constraint programming. D) goal programming. E) None of the above Answer: A 14) Typical resources of an organization include A) machinery usage. B) labor volume. C) warehouse space utilization. D) raw material usage. E) All of the above Answer: E 15) Which of the following is not a property of all linear programming problems? A) the presence of restrictions B) optimization of some objective C) a computer program D) alternate courses of action to choose from E) usage of only linear equations and inequalities Answer: C 16) A feasible solution to a linear programming problem A) must be a corner point of the feasible region. B) must satisfy all of the problem's constraints simultaneously. C) need not satisfy all of the constraints, only the non-negativity constraints. D) must give the maximum possible profit. E) must give the minimum possible cost. Answer: B 17) Which of the following is not a part of every linear programming problem formulation? Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 3 A) an objective function B) a set of constraints C) non-negativity constraints D) a redundant constraint E) maximization or minimization of a linear function Answer: D 18) When appropriate, the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and A) finding the profit at every corner point of the feasible region to see which one gives the highest value. B) moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered. C) locating the point that is highest on the graph. D) None of the above E) All of the above Answer: A 19) The mathematical theory behind linear programming states that an optimal solution to any problem will lie at a(n) ________ of the feasible region. A) interior point or center B) maximum point or minimum point C) corner point or extreme point D) interior point or extreme point E) None of the above Answer: C 20) The corner point solution method A) will always provide one, and only one, optimum. B) will yield different results from the isoprofit line solution method. C) requires that the profit from all corners of the feasible region be compared. D) requires that all corners created by all constraints be compared. E) will not provide a solution at an intersection or corner where a non-negativity constraint is involved. Answer: C 21) The simultaneous equation method is A) an alternative to the corner point method. B) useful only in minimization methods. C) an algebraic means for solving the intersection of two or more constraint equations. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 4 D) useful only when more than two product variables exist in a product mix problem. E) None of the above Answer: C 22) Consider the following linear programming problem: The maximum possible value for the objective function is A) 360. B) 480. C) 1520. D) 1560. E) None of the above Answer: C Solution Step 1 Constraint 1: 4x+3y≤480 4x+3y =480 x=0, y=160 x=120, y=0. To plot the line, please connect two points (0, 160) and (120, 0) Constraint 2: 2x+3y≤360 2x+3y =360 x=0, y=120 x=180, y=0 To plot the line, please connect two points (0,120) and (180,0) Step 2: Graph feasible solution area or feasible region. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 5 Step 3 Find all corner (extreme) points. A (0,0), B (0,120), D(120,0) Point C is an intersection of two constraint lines 4x+3y≤480 and 2x+3y≤360. 4x+3y≤480 2x+3y≤360 C(60,80). Step 4 Corner point Solution method. Compute objective function value at all corner points. Corner Point Solution Method point Objective function value 12x + 10y A(0,0) 12x + 10y=12*0+10*0=0 B(0,120) 12x + 10y=12*0+10*120=1200 C(60,80) 12x + 10y=12*60+10*80=1520 Maximum value 1520 when x=60,y=80 D(120,0) 12x + 10y=12*120+10*0=1440 Step 5. Identify the optimal solution and make a conclusion about optimal solution and the optimal objective function value. The optimal solution is x=60, y=80. The objective function value at point x=60, y=80 is 1520. 23) Consider the following linear programming problem: Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 6 The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible value for the objective function? A) 1032 B) 1200 C) 360 D) 1600 E) None of the above Answer: B 24) Consider the following linear programming problem: Which of the following points (X,Y) is not a feasible corner point? A) (0,60) B) (105,0) C) (120,0) D) (100,10) E) None of the above Answer: C 25) Two models of a product – Regular (X) and Deluxe (Y) – are produced by a company. A linear programming model is used to determine the production schedule. The formulation is as follows: The optimal solution is X = 100, Y = 0. How many units of the regular model would be produced based on this solution? A) 0 B) 100 Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 7 C) 50 D) 120 E) None of the above Answer: B 26) Consider the following linear programming problem: What is the optimum solution to this problem (X,Y)? A) (0,0) B) (50,0) C) (0,100) D) (400,0) E) None of the above Answer: B 27) Which of the following is not acceptable as a constraint in a linear programming problem (maximization)? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) None of the above Answer: A 28) Sensitivity analysis may also be called A) postoptimality analysis. B) parametric programming. C) optimality analysis. D) All of the above E) None of the above Answer: D Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 8 29) Sensitivity analyses are used to examine the effects of changes in A) contribution rates for each variable. B) technological coefficients. C) available resources. D) All of the above E) None of the above Answer: D 30) The difference between the left-hand side and right-hand side of a less-than-or-equal-to constraint is referred to as A) surplus. B) constraint. C) slack. D) shadow price. E) None of the above Answer: C 31) The difference between the left-hand side and right-hand side of a greater-than-or-equal-to constraint is referred to as A) surplus. B) constraint. C) slack. D) shadow price. E) None of the above Answer: A 32) A constraint with zero slack or surplus is called a A) nonbinding constraint. B) resource constraint. C) binding constraint. D) nonlinear constraint. E) linear constraint. Answer: C 33) The coefficients of the variables in the constraint equations that represent the amount of resources needed to produce one unit of the variable are called A) technological coefficients. B) objective coefficients. C) shadow prices. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 9 D) dual prices. E) None of the above Answer: A 34) A constraint with positive slack or surplus is called a A) nonbinding constraint. B) resource constraint. C) binding constraint. D) nonlinear constraint. E) linear constraint. Answer: A 35) Consider the following linear programming problem: The maximum possible value for the objective function is A) 360. B) 480. C) 1520. D) 1560. E) None of the above Answer: E Solution Step 1 Constraint 1: 2x+3y≤480 2x+3y =480 x=0, y=160 x=240, y=0. To plot the line, please connect two points (0, 160) and (240, 0) Constraint 2: 4x+3y≤360 4x+3y =360 x=0, y=120 x=90, y=0 To plot the line, please connect two points (0,120) and (90, 0) Step 2: Graph feasible solution area or feasible region. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 10 Step 3 Find all corner (extreme) points. A (0,0), B (0,120), C(90,0) Step 4 Corner point Solution method. Compute objective function value at all corner points. Corner Point Solution Method point Objective function value 12x + 10y maximum A(0,0) 12x + 10y=12*0+10*0=0 B(0,120) 12x + 10y=12*0+10*120=1200 Maximum value 1200 when x=0,y=120 C(90,0) 12x + 10y=12*90+10*0=1080 Step 5. Identify the optimal solution and make a conclusion about optimal solution and the optimal objective function value. The optimal solution is x=0, y=120. The objective function value at point x=0, y=120 is 1200. 36) Consider the following linear programming problem: Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 11 Which of the following points (X,Y) is feasible? A) (10,120) B) (120,10) C) (30,100) D) (60,90) E) None of the above Answer: C 37) Consider the following linear programming problem: Which of the following points (X,Y) is in the feasible region? A) (30,60) B) (105,5) C) (0,210) D) (100,10) E) None of the above Answer: D 38) Which of the following functions is not linear? A) 5X + 3Z B) 3X + 4Y + Z - 3 C) 2X + 5YZ D) Z E) 2X - 5Y + 2Z Answer: C 39) Which of the following is not one of the steps in formulating a linear program? A) Graph the constraints to determine the feasible region. B) Define the decision variables. C) Use the decision variables to write mathematical expressions for the objective function and the constraints. D) Identify the objective and the constraints. Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 12 E) Completely understand the managerial problem being faced. Answer: A 40) Which of the following is not acceptable as a constraint in a linear programming problem (minimization)? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 Answer: E 41) What type of problems use LP to decide how much of each product to make, given a series of resource restrictions? A) resource mix B) resource restriction C) product restriction D) resource allocation E) product mix Answer: E Consider the sensitivity report below for the problems which follow. 42) The optimal solution to this linear program is Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 13 A) x1 = 0, x2 = 0. B) x1 = 34, x2 = 40. C) x1 = 6, x2 = 11. D) x1 = 7.33, x2 = 6. E) x1 = 3, x2 = 6. Answer: E 43) Which of the following constraints are binding? A) Extrusion only B) Packing only C) Additive only D) Extrusion and Packaging E) All constraints are binding Answer: D 44) What is the increase in the objective value if 2 units of extrusion are added? A) 3 B) 6 C) 48 D) 96 E) Not enough information provided Answer: B 45) What is the increase in the objective value if 2 units of packaging are added? A) 11 B) 18 C) 22 D) 36 E) Not enough information provided Answer: C 46) What is the increase in the objective value if 2 units of additive is added? A) 0 B) 4 C) 12 D) 16 E) Not enough information provided Answer: A Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 14 47. Consider the sensitivity report below: (a) Which constraints are binding? (b) Which constraints are non-binding? (c) What is the increase in the objective value if 10 blades are added? Answer: (a) Bolts, Blades, and Nuts (b) Motors and Wire (c) 23.33 Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Test Item File Introduction to Management Science Bernard W. Taylor III Martha Wilson California State University , Sacramento Upper Saddle River, New Jersey 07458 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Contents Chapter 1 Management Science 1 Chapter 2 Linear Programming: Model Formulation and Graphical Solution 21 Chapter 3 Linear Programming: Computer Solution and Sensitivity Analysis 45 Chapter 4 Linear Programming: Modeling Examples 74 Chapter 5 Integer Programming 96 Chapter 6 Transportation, Transshipment, and Assignment Problems 120 Chapter 7 Network Flow Models 144 Chapter 8 Project Management 169 Chapter 9 Multicriteria Decision Making 195 Chapter 10 Nonlinear Programming 222 Chapter 11 Probability and Statistics 235 Chapter 12 Decision Analysis 265 Chapter 13 Queuing Analysis 297 Chapter 14 Simulation 320 Chapter 15 Forecasting 347 Chapter 16 Inventory Management 377 Module A The Simplex Solution Method 406 Module B Transportation and Assignment Solution Methods 426 Module C Integer Programming: The Branch and Bound Method 447 Module D Nonlinear Programming: Solution Techniques 462 Module E Game Theory 473 Module F Markov Analysis 488 Problem difficulty levels are represented as: Diff 1 - Easy Diff 2 - Moderate Diff 3 - Difficult Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Chapter 1 Management Science True/False 1) Management science involves the philosophy of approaching a problem in a subjective manner. Answer: FALSE Diff: 1 Key words: scientific approach 2) Management science encompasses a logical approach to problem solving. Answer: TRUE Diff: 1 Key words: scientific approach, problem solving 3) Once management scientist makes his or her decision and recommendation to management, then typically, his or her involvement with the problem is finished. Answer: FALSE Diff: 2 Key words: management science, management scientist 4) A variable is a symbol used to represent an item that can take on any value. Answer: TRUE Diff: 1 Key words: variable 5) Parameters are unknown, constant values that are not coefficients of variables in equations. Answer: FALSE Diff: 1 Key words: parameter 6) Data are pieces of information from the problem environment. Answer: TRUE Diff: 1 Key words: data 7) A model is a functional relationship including variables, parameters, and equations. Answer: TRUE Diff: 1 Key words: model, management science techniques 1 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 8) A management science technique usually applies to a specific model type. Answer: TRUE Diff: 1 Key words: models, management science techniques 9) A management science solution can be either a recommended decision or information that helps a manager make a decision. Answer: TRUE Diff: 1 Key words: solution, management science solution 10) Management science modeling techniques provide results that are known with certainty. Answer: FALSE Diff: 2 Key words: management science modeling techniques, certainty 11) A constraint represents the limitation of management science techniques. Answer: FALSE Diff: 2 Key words: constraints, management science techniques 12) The term decision analysis refers to testing how a problem solution reacts to changes in one or more of the model parameters. Answer: FALSE Diff: 1 Key words: sensitivity analysis, parameter changes 13) Fixed costs depend on the number of items produced. Answer: FALSE Diff: 1 Key words: fixed cost, break-even analysis 14) Variable costs are independent of volume and remain constant. Answer: FALSE Diff: 1 Key words: variable cost, break-even analysis 15) Total cost equals the fixed cost plus the variable cost per unit divided by volume. Answer: FALSE Diff: 1 Key words: total cost, break-even analysis 2 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 16) Profit is the difference between total revenue and total cost. Answer: TRUE Diff: 1 Key words: profit, break-even analysis 17) The break-even point is the volume that equates total revenue with total cost and profit is zero. Answer: TRUE Diff: 1 Key words: break-even analysis 18) In general, an increase in price increases the break even point if all costs are held constant. Answer: FALSE Diff: 1 Key words: break-even analysis 19) If variable costs increase, but price and fixed costs are held constant, the break even point will decrease. Answer: FALSE Diff: 2 Key words: break-even analysis 20) Managers utilize spreadsheets to conduct their own analyses in management science studies. Answer: TRUE Diff: 2 Key words: spreadsheets 21) Management science techniques focus primarily on 3 specific steps of the management science process (observation, model construction and implementation) to find an appropriate solution to a problem. Answer: FALSE Diff: 2 Key words: mgt sci modeling techniques, steps of the scientific method 22) Management science modeling techniques focus on model construction and problem solution. Answer: TRUE Diff: 2 Key words: mgt science model techniques, model constr, prob solution 3 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 23) Enterprise Resource Planning (ERP) system is a data oriented decision support system that utilizes specific management science solution procedures to solve individual problems such as cost-volume analysis. Answer: FALSE Diff: 1 Key words: decision support systems Fill in the Blank 24) A __________ is a symbol used to represent an item that can take on any value. Answer: variable Diff: 1 Key words: variable, management science process 25) __________ are unknown, constant values that are not coefficients of variables in equations. Answer: Parameters Diff: 1 Key words: model, parameters 26) __________ are pieces of information from the problem environment. Answer: Data Diff: 1 Key words: data 27) A __________ is a functional relationship including variables, parameters, and equations. Answer: model Diff: 1 Key words: model 28) __________ techniques consist of models that are represented as diagrams, presenting a pictorial representation of the system being analyzed. Answer: Network Diff: 1 Key words: management science, networks 29) __________ techniques provide results that contain uncertainty, unlike mathematical programming techniques which are deterministic. Answer: Probabilistic Diff: 1 Key words: management science techniques, probabilistic techniques 4 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 30) __________ are independent of volume of goods produced and remain constant. Answer: Fixed costs Diff: 1 Key words: fixed cost, break-even analysis 31) __________ depend on the number of items produced. Answer: Variable costs Diff: 1 Key words: variable cost, break-even analysis 32) __________ is the difference between total revenue and total cost. Answer: Profit Diff: 1 Key words: profit, break-even analysis 33) The __________ is the volume that equates total revenue with total cost and profit is zero. Answer: break-even point Diff: 1 Key words: break-even analysis 34) A __________ represents a limitation to achieving maximum profits due to limited resources. Answer: constraint Diff: 1 Key words: constraint, model development 35) The __________ can be noted as Z, and represents the goal of the firm. Answer: objective function Diff: 1 Key words: objective function, model development 36) A __________ is a computer-based system that helps decision-makers address complex problems that involve different parts of an organization and operations. Answer: decision support system Diff: 1 Key words: decision support systems Problem Solving 37) The relationship d = 5000 - 25p describes what happens to demand (d) as price (p) varies. Price can vary between $10 and $50. How many units can be sold when the price is $10? Answer: 4750 Diff: 1 Key words: break-even analysis 5 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 38) There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Write a mathematical expression for total cost. Answer: C(x) = 50000 + 25x Diff: 1 Key words: break-even analysis 39) There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Write an expression for total revenue. Answer: R(x) = 45x Diff: 1 Key words: break-even analysis 40) There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Write an expression for total profit. Answer: P(x) = 45x - (50000 + 25x) Diff: 1 Key words: break-even analysis 41) There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Find the break -even point. Answer: X = 2500 Diff: 2 Key words: break-even analysis 42) Administrators at a university will charge students $150 to attend a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. How many students would have to register for the seminar for the university to break even? Answer: 24 Diff: 2 Key words: break-even analysis 43) Administrators at a university are planning to offer a summer seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? Answer: $175 Diff: 2 Key words: break-even analysis 6 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 44) A newly opened bed-and-breakfast projects the following: Monthly fixed costs $6000 Variable cost per occupied room per night $20 Revenue per occupied room per night $75 Write the expression for total cost per month (30 days). Answer: C(x) = 6000 + 20(30)x Diff: 2 Key words: break-even analysis 45) A newly opened bed-and-breakfast projects the following: Monthly fixed costs $6000 Variable cost per occupied room per night $20 Revenue per occupied room per night $75 Write the expression for total revenue per month (30 days). Answer: R(x) = 75(30)x Diff: 2 Key words: break-even analysis 46) A newly opened bed-and-breakfast projects the following: Monthly fixed costs $6000 Variable cost per occupied room per night $20 Revenue per occupied room per night $75 If there are 12 rooms available, what percentage of rooms would have to be occupied, on average, to break even? Answer: 3.64 = 4 rooms - 4/12 = 33% Diff: 3 Key words: break-even analysis 47) A script writer has received an advance against royalties of $10000. The royalty rate is $1 for every performance in the US, and $1.35 for every performance outside the US. Define variables for this problem. Answer: X1 = # of performances in the U.S. X2 = # of performances outside the U.S. Diff: 3 Key words: break-even analysis 48) A script writer has received an advance against royalties of $10,000. The royalty rate is $1 for every performance in the US, and $1.35 for every performance outside the US. Write an expression that could be used to compute the number of performances in order to cover the advance. Answer: 10000 = 1x 1 + 1.35x2 Diff: 3 Key words: break-even analysis 7 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 49) Students are organizing a ʺBattle of the Bandsʺ contest. They know that at least 100 people will attend. The rental fee for the hall is $150 and the winning band will receive $500. In order to guarantee that they break even, how much should they charge for each ticket? Answer: $6.50 Diff: 2 Key words: break-even analysis 50) A manufacturer buys peas for vegetable pies from 2 cooperatives. The price per unit is $6 from cooperative A, and $5.50 per unit from cooperative B. Define variables that would tell how many units to purchase from each source. Answer: X1 = # of units from cooperative A X2 = # of units from cooperative B Diff: 3 Key words: break-even analysis, variable definition 51) A manufacturer buys peas for vegetable pies from 2 cooperatives. The price per unit is $6 from cooperative A, and $5.50 per unit from cooperative B. Develop an objective function that would minimize the total cost. Answer: Min 6x 1 + 5.5x2 Diff: 3 Key words: objective function, break-even analysis, model development 52) A manufacturer buys peas for vegetable pies from 2 cooperatives. The price per unit is $6 from cooperative A, and $5.50 per unit from cooperative B. The manufacturer needs at least 12000 units of peas. Cooperative A can supply up to 8000 units, and cooperative B can supply at least 6000 units. Develop constraints for these conditions. Answer: XA + XB ≤ 12000 XA ≤ 8000 XB ≥ 6000 Diff: 3 Key words: constraints, model development 53) A manager of the cereal bar at the college campus has determined that the profit made for each bowl of Morning Buzz cereal sold, x, is equal to: Z = $4x - 0.5x. Each bowl of Morning Buzz weighs 6 ounces, and the manager has 12 lbs (192 ounces) of cereal available each day, which can be written as the constraint, 6x ≤192. How much profit will be made from Morning Buzz if it is all sold in one day? Answer: $112 Diff: 2 Key words: model development 8 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 54) The College Coffee Cafe buys tea from 3 suppliers. The price per pound is $15.00 from supplier A, $17.50 from supplier B, and $21.00 from supplier C. They have budged $175 to purchase the tea. The cafe needs at least 12 pounds of tea, and supplier C can supply no more than 4 pounds. Develop constraints for these conditions. Answer: 15.00XA + 17.50 X B + 21XC ≤175 XA +XB +XC ≥ 12 XC ≤ 4 Diff: 3 Key words: constraints, model development 55) The College Coffee Cafe receives a profit of $1.25 for each cup of house tea that they sell, $1.40 for each cup of the premium brand, and $1.50 for each cup of their special blend that they sell. Develop an objective that maximizes profit. Answer: Max 1.25x 1 + 1.40x2 + 1.50 x3 Diff: 2 Key words: objective function, model development Multiple Choice 56) The steps of the scientific method are: A) problem definition, model construction, observation, model solution, implementation. B) observation, problem definition, model construction, model solution, implementation. C) model construction, problem definition, observation, model solution, implementation. D) observation, implementation, problem definition, model construction, model solution. Answer: B Diff: 1 Key words: steps of sci method, prob solving approach, mgt sci process 57) A model is a functional relationship and include: A) variables B) parameters C) equations D) all of the above Answer: D Diff: 1 Key words: model 9 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 58) Which of the following is an equation or an inequality that expresses a resource restriction in a mathematical model? A) a decision variable. B) data C) an objective function. D) a constraint. E) a parameter. Answer: D Diff: 2 Key words: model, constraint 59) Which of the following is incorrect with respect to the use of models in decision making? A) they improve understanding of the problem B) they promote subjectivity in decision making C) they are generally easy to use D) they provide a systematic approach to problem solving Answer: B Diff: 3 Key words: model, problem solving 60) The field of management science A) approaches decision making rationally with techniques based on the scientific method B) is another name for decision science and for operations research C) concentrates on the use of quantitative methods to assist managers in decision making D) all of the above Answer: D Diff: 1 Key words: management science, operations research 61) The processes of problem observation A) cannot be done until alternatives are proposed B) requires consideration of multiple criteria C) is the first step of decision making D) is the final step of problem solving Answer: C Diff: 1 Key words: observation, problem observation, management science process 10 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 62) The limits of the problem and the degree to which it pervades other units other units in the organization must be included during the __________ step of the management science process. A) observation B) definition C) solution D) implementation Answer: B Diff: 1 Key words: management science process 63) __________ involves determining the functional relationship between variables, parameters and equations A) Problem observation B) Problem definition C) Model construction D) Model solution E) Model implementation Answer: C Diff: 1 Key words: management science process, model construction 64) Management science __________ can either be a recommended decision or information that helps a manager make a decision. A) model implementation B) model construction C) problem definition D) model solution E) problem formulation Answer: D Diff: 2 Key words: management science process, model solution 65) The quantitative analysis approach requires A) mathematical expressions for the relationship B) uncomplicated problems C) the manager to have prior experience with similar problems D) all of the above Answer: A Diff: 2 Key words: management science, operations research, quantitative analysis 11 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 66) The result of an effective decision making process should be monitored in order to A) reveal wrong assumptions B) reveal errors in the implementation C) insure the achievement of desired results D) all of the above Answer: D Diff: 2 Key words: decision making process 67) Which of the following is not a general approach to decision-making? A) establishing priorities B) analysis of tradeoffs C) an emphasis on subjectivity D) a systemʹs approach Answer: C Diff: 2 Key words: decision making, management science 68) The management science process does not include A) problem definition B) feedback C) implementation D) subjective preference E) information Answer: D Diff: 2 Key words: management science process 69) The indicator that results in total revenues being equal to total cost is called the A) marginal cost B) marginal volume C) break-even point D) profit mix Answer: C Diff: 1 Key words: break-even analysis 12 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com) lOMoARcPSD|26927854 Management Science - Chapter 1 70) Variable cost A) depends on the number of units produced B) plus marginal cost equals fixed cost C) is equal to total cost in deterministic models D) all of the above Answer: A Diff: 2 Key words: break-even analysis 71) The components of break-even analysis are A) volume, cost and profit B) volume and cost C) cost and profit D) volume and profit Answer: A Diff: 1 Key words: break-even analysis 72) __________ are generally independent of the volume of units produced and sold. A) Fixed costs B) Variable costs C) Profits D) all of the above Answer: A Diff: 1 Key words: break-even analysis 73) The purpose of break-even analysis is to determine the number of units of a product to sell that will A) equal total revenue with total cost B) be larger than total revenue compared to total cost C) be smaller than total revenue compared to total cost D) none of the above Answer: A Diff: 2 Key words: break-even analysis 13 Full file at http://testbank360.eu/test-bank-introduction-to-management-science-9th-edition-taylor Downloaded by ?? Hu?nh Thanh Th?o (thaodo0510@gmail.com)
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