# Question

Consider the Union Airways problem presented in Sec. 3.4, including the data given in Table 3.19. The Excel files for Chap. 3 include a spreadsheet that shows the formulation and optimal solution for this problem. You are to use this spreadsheet and Solver to do parts (a) to (g) below. Management is about to begin negotiations on a new contract with the union that represents the company's customer service agents. This might result in some small changes in the daily costs per agent given in Table 3.19 for the various shifts. Several possible changes listed below are being considered separately. In each case, management would like to know whether the change might result in the solution in the spreadsheet no longer being optimal. Answer this question in parts (a) to (e) by using the spreadsheet and Solver directly. If the optimal solution changes, record the new solution.

(a) The daily cost per agent for Shift 2 changes from $160 to $165.

(b) The daily cost per agent for Shift 4 changes from $180 to $170.

(c) The changes in parts (a) and (b) both occur.

(d) The daily cost per agent increases by $4 for shifts 2, 4, and 5, but decreases by $4 for shifts 1 and 3.

(e) The daily cost per agent increases by 2 percent for each shift.

(f) Use Solver to generate the sensitivity report for this problem. Suppose that the above changes are being considered later without having the spreadsheet model immediately available on a computer. Show in each case how the sensitivity report can be used to check whether the original optimal solution must still be optimal.

(g) For each of the five shifts in turn, use a parameter analysis report to systematically generate the optimal solution and total cost when the only change is that the daily cost per agent on that shift increases in $3 increments from $15 less than the current cost up to $15 more than the current cost.

(a) The daily cost per agent for Shift 2 changes from $160 to $165.

(b) The daily cost per agent for Shift 4 changes from $180 to $170.

(c) The changes in parts (a) and (b) both occur.

(d) The daily cost per agent increases by $4 for shifts 2, 4, and 5, but decreases by $4 for shifts 1 and 3.

(e) The daily cost per agent increases by 2 percent for each shift.

(f) Use Solver to generate the sensitivity report for this problem. Suppose that the above changes are being considered later without having the spreadsheet model immediately available on a computer. Show in each case how the sensitivity report can be used to check whether the original optimal solution must still be optimal.

(g) For each of the five shifts in turn, use a parameter analysis report to systematically generate the optimal solution and total cost when the only change is that the daily cost per agent on that shift increases in $3 increments from $15 less than the current cost up to $15 more than the current cost.

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