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
Demin Jeans
CD player
Compact discs
Weight (lb)
2
3
1
Profit
$ 90
150
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)
1
2
3
4
5
6
7
8
50
105
56
45
90
80
78
60
Management
scientists require
6
8
9
3
7
5
8
5
Estimated profit
(1,000,000s)
0.30
0.85
0.20
0.15
0.50
0.45
0.55
0.40
Formulate the integer programming model for this problem and solve it using the
computer.
