BASED ON CHAPTERS 1 - 3 Constraints limit the alternatives available to a decision maker. → TRUE Linear programming problems may have multiple goals or objectives specified. → FALSE An example of a decision variable in a linear programming problem is profit maximization. → FALSE The equation 5x + 7y = 10 is linear. → TRUE The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits. What is the objective function? → P = 2A + B ● Since the objective is to maximize profits, the objective function should reflect the profitability of A ($2.00 per pound) and B ($1.00 per pound). What is the constraint for Colombian beans? → 12A + 8B ≤ 4,800. ● Since each pound of A uses 12 ounces of Colombian beans and each pound of B uses 8 ounces of Colombian beans, it is convenient to convert the supply of Colombian beans to ounces (300 pounds = 4,800 ounces). Then the constraint should reflect that the usages (12 ounces per pound of A, 8 ounces per pound of B) must be less than the supply. A linear programming problem may return fractional solutions (e.g. 4 1/3) for a resource allocation problem. → TRUE Linear programming does not permit fractional solutions. → FALSE A freelance writer must choose how to spend her time working on several different types of projects. Newspaper stories take 3 hours to write and pay a flat rate of $45 per story. Magazine articles take much longer to write (25 hours) but pay significantly better ($400 per article). Proofreading is often tedious, but the writer can always find proofreading jobs that pay $20 per hour. The writer wants to maximize her income, but doesn't want to work more than 45 hours per week. Additionally, she dislikes proofreading so she would like to spend no more than 7 hours per week on that task. Both newspaper stories and magazine articles must be completed in the week they are started (HINT: use an integer constraint to be sure that all newspaper and magazine jobs are finished within a week). The writer's problem falls within which classification? → Resource-allocation. Which of the following is the objective function for the writer's problem? → Max R = 45N + 400M + 20P A local maximum is always a global maximum in a nonlinear programming problem. → FALSE A quadratic programming problem is a special type of linear programming problem. → FALSE Linear programming assumes that the profit from each activity is proportional to the level of that activity. → TRUE A nonlinear function may contain a product of two variables. → TRUE Profit = 3x1 + 2x2 + 9x1x2 is an example of a nonlinear function. → TRUE When applying nonlinear programming to portfolio selection, a trade-off is being made between the expected return and the risk associated with the investment. → TRUE Orange = objective cells, blue = given , yellow = changing cells and constraints (? ) Three types of analytics: 1. Descriptive (analyzing data to improve descriptions of what has been happening) 2. Predictive (predictive models to improve predictions of what is likely to happen in future) 3. Prescriptive (prescriptive models, including optimization models, to improve managerial decision making) Constraint: an inequality or equation in a mathematical model that expresses some restricitions on the values that can be assigned to the decision variable aka boundaries Product mix problem: A type of linear programming problem where the objective is to find the most profitable mix of production levels for the products under consideration. SUMPRODUCT function is used extensively in linear programming spreadsheet modals Solution: Any single assignment of values to the decision variables, regardless of whether the assignment is a good one or even a feasible one. A feasible solution is one that satisfies all the constraints, whereas an infeasible solution violates at least one constricturant Optimal solution: a feasible solution that results in the largest possible objective function value when maximizing (or smallest when minimizing). The best feasible solution is called optimal solution (maximizes) Feasible religion: points that satifty every constraint Types of linear programing: ● Resource allocation problems ○ problems involving the allocation of resourcres to activities ● Cost benefit trade off problems ○ problemswhere the mix of levels of various activities is chosen to achieve minimum acceptable levels for various benefits at a minimum cost ● Transportation problems ○ problem a that typically involves finding a shipping plan that minimizes the total cost of transportaying a product from anumber of plants to a number of customers ● Assignment problems ○ problem that typically involves assigning people to tasks so as to minisize the total cost of performing these tasks ● Fixed requirements problem ○ Problem concencerned with optimazing how to meet a number of fixed requirements ● Integer ptogtamming problem ○ Problem that has the additional restriction that some or all of the decision variables must have integer values The best feasible solution is called → optimal solution. When using the graphical method, the region that satisfies all of the constraints of a linear programming problem is called the → feasible region. Resource-allocation problems are linear programming problems involving the → allocation of limited resources to activities. For cost-benefit-tradeoff problems, minimum acceptable levels for each kind of benefit are prescribed and the objective → is to achieve all these benefits with minimum cost.
