A manager wants to know how many units of each product to produce on a daily basis in order to achieve the highest contribution to profit. The production requirements for the products are shown in the following table.
Material 1 costs $ 5 a pound, material 2 costs $ 4 a pound, and labor costs $ 10 an hour. Product A sells for $ 80 a unit, product B sells for $ 90 a unit, and product C sells for $ 70 a unit. Available resources each day are 200 pounds of material 1; 300 pounds of material 2; and 150 hours of labor.
The manager must satisfy certain output requirements: The output of product A should not be more than one- third of the total number of units produced; the ratio of units of product A to units of product B should be 3 to 2; there is a standing order for 5 units of product A each day. Formulate a linear programming model for this problem, and then solve it.