运筹学课后答案5

CHAPTER 5

WHAT-IF ANALYSIS FOR LINEAR PROGRAMMING

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.

5-1

5.4-1 The 100% rule considers the percentage of the allowable change (increase or decrease) for each

coefficient in the objective function. 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-hand-sides,

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.

5-2

5.6-4 The right-hand sides of the constraints often represent managerial policy decisions. These

decisions are frequently interrelated and so need to be considered simultaneously. 5.6-5 The 100 percent rule basically says that we can safely use the shadow prices to predict the effect

of simultaneous changes in the right-hand sides if the sum of the percentages of the changes does not exceed 100 percent. 5.6-6 The data needed to apply the 100% rule for simultaneous changes in right-hand sides are given by

the Sensitivity Report (Constraint R.H. Side, Allowable Increase, and Allowable Decrease). 5.6-7 If the …… 此处隐藏：16654字，全部文档内容请下载后查看。喜欢就下载吧 ……