Problem 2. Integer Programming Modeling and Implementation (12 points)

Northeastern Airlines (NEA) is considering expanding its operation in which it will purchase new aircraft for its European routes. NEA is looking at the purchase of Boeing B797s and Airbus A450. The budget allocated for purchases is $800 million. Boeing B797s cost $40 million a piece and Airbus A450s cost $30 million each. NEA has allocated another $10 million for the additional personnel hires to support the operation of the new planes. Each B797 requires $400,000 in new personnel hires and each A450 requires $350,000. On average, each of these planes are expected to generate an annual profit of $3.5 million and $2.7 million respectively (net of plane cost, personnel cost, maintenance cost, fuel cost, etc.).

In an effort to achieve some uniformity with respect to fleet appearance, spare parts and maintenance procedures, NEA executives have specified that they will not buy fewer than 10 airplanes of any type. Their objective is to maximize total annual profit.

Currently, the available maintenance facilities allow 600 days of maintenance per year for newly purchased planes. Each B797 requires 45 days of annual maintenance and each A450 requires 35 days. However, it is possible to increase the available maintenance time to 900 days. To accomplish this, the maintenance facilities would have to be expanded at a cost of $16 million, which will come out of the budget for new plane purchase. In addition, the expansion would increase operating costs by $18 million annually, an expense that would reduce annual profit.

Writing below in plain words, what are the decisions that NEA is trying make and what is the objective that NA wants to achieve? (2 points)

Write out the detail and explicit mathematical optimization problem below by clearly defining the decision variables (0.5 point), the objective function (0.5 point) and all needed constraints (3 points) [Total 4 points]

Implement the optimization problem in Excel. Label the worksheet as Prob 2 (4 points)

What is the optimal decision? (1 point)

The optimal decision is to .

What is the optimal annual profit? (1 point) Optimal annual profit = $...