# Model 20: Production Capacity Adjustment

A manufacturing firm 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:

Machine type Available time
(in 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 \$30, \$12, and \$15, respectively, on products 1, 2, and 3. The objective is to determine how much of each product the firm should produce to maximize profit.

Formulate the linear programming model for this problem.