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