MAT540 Week 9 Homework Chapter 5 Juan Hernandez, a Cuban athlete

MAT540 

Week 9 Homework 

Chapter 5 

• 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 weight and profit (in U.S. dollars) of each item are as follows: 

Item  

Weight (lb.) 

Profit  

Denim jeans 

2 

$90 

CD players 

3 

150 

Compact discs 

1 

30 

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 and solve the problem. 

• The Texas Consolidated Electronics Company is contemplating a research and development program encompassing eight research projects. The company is constrained from embarking on all projects by the number of available management scientists (40) and the budget available for R&D projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice versa). Following are the resources requirement and the estimated profit for each project. 

Project  

Expense ($1,000s) 

Management 

Scientists required 

Estimated Profit 

(1,000,000s) 

1 

50 

6 

0.30 

2 

105 

8 

0.85 

3 

56 

9 

0.20 

4 

45 

3 

0.15 

5 

90 

7 

0.50 

6 

80 

5 

0.45 

7 

78 

8 

0.55 

8 

60 

5 

0.40 

Formulate the integer programming model for this problem and solve it using the computer. 

• Corsouth Mortgage Associates is a large home mortgage firm in the southeast. It has a poll of permanent and temporary computer operators who process mortgage accounts, including posting payments and updating escrow accounts for insurance and taxes. A permanent operator can process 220 accounts per day, and a temporary operator can process 140 accounts per day. On average, the firm must process and update at least 6,300 accounts daily. The company has 32 computer workstations available. Permanent and temporary operators work 8 hours per day. A permanent operator averages about 0.4 error per day, whereas a temporary operator averages 0.9 error per day. The company wants to limit errors to 15 per day. A permanent operator is paid $120 per day wheras a temporary operator is paid $75 per day. Corsouth wants to determine the number of permanent and temporary operators it needs to minimize cost. Formulate, and solve an integer programming model for this problem and compare this solution to the non-integer solution.