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:
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 this problem by defining the decision variables, objective function, and all the constraints. Do NOT solve after formulating.