The Omega Manufacturing Company has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity. Management is considering devoting this excess capacity to one or more of three products; call them products 1, 2, and 3. The available capacity on the machines that might limit output is summarized in the following table:

The number of machine hours required for each unit of the respective products is

The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 units per week. The unit profit would be $50, $20, and $25, respectively, on products 1, 2, and 3. The objective is to determine how much of each product Omega should produce to maximize profit.
(a) Formulate a linear programming model for this problem.
(b) Use a computer to solve this model by the simplex method.

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Available Time Machine Type (Machine Hours per Week) Milling machine Lathe Grinder 500 350 150 Productivity coefficient (in machine hours per unit) Product 1 Product 2 Product 3 Milling machine Lathe Grinder