Find the Optimal Purchasing Plan using Integer Programming

1. Buying equipment.

Oriental Airlines is considering a capital expansion in which it will purchase new aircraft for its Pacific runs. Oriental is looking at the purchase of Boeing B797s, Airbus A450s and Lockheed L120s. The budget for new purchases is $750 million. Boeing B797s cost $42 million, Airbus A450s cost $30 million, and Lockheed L120s cost $27.5 million. On the average these planes are expected to generate annual profits of $3.5 million, $2.8 million, and $3.0 million, respectively. In an effort to achieve some uniformity with respect to spare parts and maintenance procedures, airline executives have specified that they will not buy fewer than 10 airplanes of any type. Their objective is to maximize total annual profit.

Oriental has allocated up to $10 million for additional personnel to support the operation of the new aircraft. Each B797 requires $200,000 in new hires; each A 450 requires $180,000; and each L120 requires $190,000.

Currently the available maintenance facilities allow 800 days of maintenance per year for new purchases. Each B797 requires 45 days of annual maintenance; each A450 requires 38 days; and each L120 requires 42 days. It is possible, however to increase the available annual maintenance to 1,250 days. To accomplish this, the maintenance facilities would have to be expanded at a capital cost of $16 million, which would come out of the budget for new purchases. In addition, the expansion would augment operating costs by $18 million annually, an expense that would reduce annual profits.

a. What is the optimal purchasing plan, and what is the corresponding annual profit for Oriental?
b. Suppose the maintenance expansion were to augment operating cost $24 million instead of $18 million. Then, what would be the optimal purchasing plan?
c. Suppose that, in addition to the augmented operating cost of $24 million, the uniformity policy required a minimum of only 8 airplanes of the same type rather than 10 as at present. What would be the optimal purchasing plan under these assumptions?