The Midland Tool Shop has four heavy presses it uses to stamp out prefabricated metal covers and housings for electronic consumer products. All four presses operate differently and are of different sizes. Currently the firm has a contract to produce three products. The contract calls for 400 units of product 1; 570 units of product 2; and 320 units of product 3. The time (in minutes) required for each product to be produced on each machine is as follows:

Machine 1 is available for 150 hours, machine 2 for 240 hours, machine 3 for 200 hours, and machine 4 for 250 hours. The products also result in different profits, according to the machine they are produced on, because of time, waste, and operating cost. The profit per unit per machine for each product is summarized as follows:

The company wants to know how many units of each product to produce on each machine in order to maximize profit.
a. Formulate this problem as a linear programming model.
b. Solve the model by using thecomputer.

Machine Product 35 41 3439 40 36 32 43 38 37 33 40 2 Machine Product 1 4 $7.8 $7.8 $8.2 $7.9 6.3 5.8 6.7 8.4 8.9 8.1 9.2 9.0