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:

92 3 INTRODUCTION TO LINEAR PROGRAMMING Available Time Machine Type (Machine Hours per Week)

Milling machine 500 Lathe 350 Grinder 150 The number of machine hours required for each unit of the respective products is Productivity coefficient (in machine hours per unit)

Machine Type Product 1 Product 2 Product 3 Milling machine 9 3 5 Lathe 5 4 0 Grinder 3 0 2 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.
C

(b) Use a computer to solve this model by the simplex method.