A type of problem most often identified with the linear program is the problem of distributing scarce resources among alternative activities. In this example the scarce resources are time availabilities for four machines and the alternative activities are the production volumes of five products. The machine requirements in hours per unit are shown for each product in the table below. With the exception of product 4, that does not require machine 1, each unit of product must pass through all four machines. The unit profits for each product are also shown in the table. There are four machines of type 1, five of type 2, three of type 3 and seven of type 4. Each machine operates 40 hours per week. The linear programming model is to determine the optimum weekly production quantities for the products. The goal is to maximize total profit.
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