Quantitative Analysis for Management

1. Bakery produces muffins and doughnuts. Let x1 be the number of doughnuts produced and x2 be the number of muffins produced.

The profit function for the bakery is expressed by the following equation: profit = 4x1 + 2x2 + 0.3x12 + 0.4x22.

The bakery has the capacity to produce 800 units of muffins and doughnuts combined and it takes 30 minutes to produce 100 muffins and 20 minutes to produce 100 doughnuts. There is a total of 4 hours available for baking time. There must be at least 200 units of muffins and at least 200 units of doughnuts produced. Formulate a nonlinear program representing the profit maximization problem for the bakery.

2. A package express carrier is considering expanding the fleet of aircraft used to transport packages. Of primary importance is that there is a total of $350 million allocated for purchases. Two types of aircraft may be purchased - the C1A and the C1B. The C1A costs $25 million, while the C1B costs $18 million. The C1A can carry 60,000 pounds of packages, while the C1B can only carry 40,000 pounds of packages. Of secondary importance is that the company needs at least 10 new aircraft. It takes 150 hours per month to maintain the C1A, and 100 hours to maintain the C1B. The least level of importance is that there are a total of 1,200 hours of maintenance time available per month.

Part 1: Formulate this as an integer programming problem to maximize the number of pounds that may be carried.

Part 2: Rework the problem differently than in Part 1 to suppose the company decides that what is most important to them is that they keep the ratio of C1Bs to C1As in their fleet as close to 1.2 as possible to allow for flexibility in serving their routes. Formulate the goal programming representation of this problem, with the other three goals having priorities P2, P3, and P4, respectively.