The scenario is the same as for HW-9. The questions are from the topic "sensitivity in Linear Programming":

A refrigerator manufacturer makes 3 models: Mini, Standard, and Large. Upon selling these products, the profit realized per unit is:

          Mini:           $150

          Standard:    $200

          Large:         $250

In order to produce each model, the parts requirements are as follows:

                   Number of            Number of            Manufacturing

                   Grill covers          Ice Makers            Time (hours)

Mini                     1                           1                           6

Standard             1                           2                           10

Large                  2                           2                           15

During the next manufacturing cycle, the inventory department has 600 Grill Covers and 800 Ice Makers in stock. The factory has 3000 hours of manufacturing time available.

The linear programming model for the problem is:

          Max (150M + 200S + 250L)

          s.t.     1M + 1S + 2L       <       600             Grill Covers

                   1M +   2S +   2L   <       800             Ice Makers

                   6M + 10S + 15L   <       3000           Manufacturing Time

                   M, S, L > 0

The solution to the above LP problem and the Sensitivity Report (using MS Excel) are presented on the page 3.

Questions (your answers MUST include reasons based on the Excel solution on page 3):

1.     If the profit for the Large model increased to $300, would the optimal solution change?

2.     If the profit for the Mini model is reduced to $125 and the profit for the Standard Model is increased to $240 simultaneously and the profit for the Large model stayed at $250, would the optimal solution change?

3.     Use MS Excel to solve the modified problem in part 2 and submit a printout of your results - mark it up by hand to identify the impact (if any) to the original solution.

4.     If the number of Grill Covers available in stock dropped from 600 to 550 what difference will it make to the maximum profit as long as none of the other resources change?

5.     If the number of Ice Makers available in stock doubled from 800 to 1600 what difference will it make to the maximum profit as long as none of the other resources change?

6.     If the company increased its capacity to 3500 manufacturing hours, without change in any other resources, will maximum profit change? By how much?

7.     If the number of Ice Makers available in stock was reduced from 800 to 600, and the number of manufacturing hours increased from 3000 to 3180, what will be the impact on total profit? Assume that there is no change to the number of Grill Covers in stock.