# Discussion Board Integer Programming Problems

### Question Description

For this discussion topic each student is required to have at least 2 postings: One answering at least one of the questions and a second responding to another studentâs posting. Please select a question that has not been answered by the time you post your response. You can select any question to answer once all questions are answered. Please do not copy another studentâs posting.

This discussion will close at midnight Sunday, November 11th.

1. Solve the following integer programming model by using a computer software:

Maximize Z = 5×1 + 6×2

Subject to

3×1 + 4×2 < 10

4×1 + 2×2 < 15

x1, x2 > 0 and integer

2. Juan Hernandez, a Cuban athlete who visits the United States and Europe frequently, is allowed to return with a limited number of consumer items not generally available in Cuba. The items, which are carried in a duffel bag, cannot exceed a weight of 5 pounds. Once Juan is in Cuba, he sells the items at highly inflated prices. The three most popular items in Cuba are denim jeans, CD players, and CDs of U.S. rock groups. The weight and profit (in U.S. dollars) of each item are as follows:

ItemWeight (lb.)Profit

Denim jeans2\$90

CD players3150

Compact discs130

Juan wants to determine the combination of items he should pack in his duffel bag to maximize his profit. This problem is an example of a type of integer programming problem known as a “knapsack” problem. Formulate this problem by defining the decision variables, objective function, and all the constraints. Do NOT solve after formulating.

3. Consider a capital budgeting example with five projects from which to select.Let Xi = 1 if project i is selected, 0 if not, for i = 1, 2, 3, 4, 5.Write the appropriate constraint(s) for each of the following conditions.Conditions are independent of one another.

(a) Select no fewer than three projects.

(b) If project 3 is selected, then project 4 must also be selected.

(c) Projects cost 150, 150, 90, 275, and 200 respectively.The budget is 400.

(d) No more than two of the five projects can be selected.

4. The Charm City Consulting has four projects to consider.Each will require time (weeks) in the next two months according to the table below. Profit from each project is also shown in the table below.

ProjectWeeks required in Month 1Weeks required in Month 2Profit in dollars

_______________________________________________________________________

121015000

241025000

3545000

46520500

There is 30 weeksâ time available in the first month and 25 weeksâ in the second month.

Formulate a zero-one integer programming problem to maximize total profit for this situation by defining the decision variables, objective function, and all the constraints.. Do NOT solve after formulating.

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