Bill\'s company makes three types of products (Product #1, Product #2, and Produ
ID: 3223117 • Letter: B
Question
Bill's company makes three types of products (Product #1, Product #2, and Product #3). These products are made of two materials (Materials A and B), and must be processed on three types of machines (Machines I, II, and Ill). Because Bill's company is going to terminate these three products soon and introduce new products, they are not going to replenish materials A and B from now on. However, the company would like to utilize the remaining inventory of materials A and B to make products #1, #2, and #3 to maximize the profit. The three machines can be made available to producing these products with a limited amount of time, and there is still a minimum number of product #3 that must be produced to satisfy a pre-existing contract with a retailer. Bill has formulated the relevant optimization problem and solve it in Solver. He produced the following sensitivity report. Use the sensitivity report to answer the following questions. A) What is the maximum profit at the optimal solution? B) If the minimum number of product #3 that must be produced is 45 rather than 30, how will the optimal profit change in direction? C) Suppose the profit of product #2 is increased to $15, will the optimal production plan change? D) Will the optimal objective function value change if Machine I's available time is decreased by 1000? If yes, in which direction? E) Will the optimal objective function value change if Machine II's available time is doubled? If yes, in which direction?Explanation / Answer
A) maximum profit at the optimal solution . is (15*30 + 12*0 + 30*10) = 750
B) remains same because The allowable decrease of the first constraint is 15 to 0. This means that even if we increasethe value by 15 the optimal condition must not change. . So, 'Remains same' is the answer.
C) YES . The allowable increase of the second variable is 6.75. So, if we increase the value more than 6.75 (say 15 as given) the optimal solution will definitely change.
D) NO. The allowable increase is near to infinity (1E+30). The machines available time can be increased without bound and there will be no change in optimality.
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