Juan hernandez, a cuban athlete who visits the united states and

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1. 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
Demin Jeans
2
$ 90
CD player
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.

1. 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 require
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.