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ALL TEST BANK Decision - final exam
Decesion MAking (‫دوعس كلملا ةعماج‬‎)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Hours
Covered
31
31
31
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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?
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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.
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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.
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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:
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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
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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
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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.
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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.
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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:
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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.
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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
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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
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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
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Test Item File
Introduction to
Management Science
Bernard W. Taylor III
Martha Wilson
California State University , Sacramento
Upper Saddle River, New Jersey 07458
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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