CHAPTER 5 WHAT-IF ANALYSIS FOR LINEAR PROGRAMMING Review Questions 5.1-1 The parameters of a linear programming model are the constants (coefficients or right-hand sides) in the functional constraints and the objective function. 5.1-2 Many of the par

CHAPTER 5 WHAT-IF ANALYSIS FOR LINEAR PROGRAMMING

Review Questions

5.1-1 The parameters of a linear programming model are the constants (coefficients or right-hand sides) in the functional constraints and the objective function. 5.1-2 Many of the parameters of a linear programming model are only estimates of quantities that cannot be determined precisely and thus result in inaccuracies. 5.1-3 What-if analysis reveals how close each of these estimates needs to be to avoid obtaining an erroneous optimal solution, and therefore pinpoints the sensitive parameters where extra care is needed to refine their estimates. 5.1-4 No, if the optimal solution will remain the same over a wide range of values for a particular coefficient, then it may be appropriate to make only a fairly rough estimate for a parameter of a model. 5.1-5 Conditions that impact the parameters of a model, such as unit profit, may change over time and render them inaccurate. 5.1-6 If conditions change, what-if analysis leaves signposts that indicate whether a resulting change in a parameter of the model changes the optimal solution. 5.1-7 Sensitivity analysis is studying how changes in the parameters of a linear programming model affect the optimal solution. 5.1-8 What-if analysis provides guidance about what the impact would be of altering policy decisions that are represented by parameters of a model. 5.2-1 The estimates of the unit profits for the two products are most questionable. 5.2-2 The number of hours of production time that is being made available per week in the three plants might change after analysis. 5.3-1 The allowable range for a coefficient in the objective function is the range of values over which the optimal solution for the original model remains optimal. 5.3-2 If the true value for a coefficient in the objective function lies outside its allowable range then the optimal solution would change and the problem would need to be resolved. 5.3-3 The Objective Coefficient column gives the current value of each coefficient. The Allowable Increase column and the Allowable Decrease Column give the amount that each coefficient may differ from these values to remain within the allowable range for which the optimal solution for the original model remains optimal. 5.4-1 The 100% rule considers the percentage of the allowable change (increase or decrease) for each coefficient in the objective function.

5-1

5.4-2 If the sum of the percentage changes do not exceed 100% then the original optimal solution definitely will still be optimal. 5.4-3 No, exceeding 100% may or may not change the optimal solution depending on the directions of the changes in the coefficients. 5.5-1 The parameters in the constraints may only be estimates, or, especially for the right-handsides, may well represent managerial policy decisions. 5.5-2 The right-hand sides of the functional constraints may well represent managerial policy decisions rather than quantities that are largely outside the control of management. 5.5-3 The shadow price for a functional constraint is the rate at which the value of the objective function can be increased by increasing the right-hand side of the constraint by a small amount. 5.5-4 The shadow price can be found with the spreadsheet by increasing the right-hand side by one, and then re-solving to determine the increase in the objective function value. It can be found similarly with a Solver Table by creating a table that shows the increase in profit for a unit increase in the right-hand side. The shadow price is given directly in the sensitivity report. 5.5-5 The shadow price for a functional constraint informs management about how much the total profit will increase for each extra unit of a resource (right-hand-side of a constraint). 5.5-6 Yes. The shadow price also indicates how much the value of the objective function will decrease if the right-hand side were to be decreased by 1. 5.5-7 A shadow price of 0 tells a manager that a small change in the right-hand side of the constraint will not change the objective function value at all. 5.5-8 The allowable range for the right-hand side of a functional constraint is found in the Solver’s sensitivity report by using the columns labeled “Constraint R.H. Side”, “Allowable increase”, and “Allowable decrease”. 5.5-9 The allowable ranges for the right-hand sides are of interest to managers because they tell them how large changes in the right-hand sides can be before the shadow prices are no longer applicable. 5.6-1 There may be uncertainty about the estimates for a number of the parameters in the functional constraints. Also, the right-hand sides of the constraints often represent managerial policy decisions. These decisions are frequently interrelated and so need to be considered simultaneously. 5.6-2 The spreadsheet can be used to directly determine the impact of several simultaneous changes. Simply change the paremeters and re-solve. 5.6-3 Using Solver Table, trial values can be enumerated simultaneously for one or two data cells, with the possibility of entering formulas for additional data cells in terms of these one or two data cells.

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