A corporation has a division that produces two models of fireplace grates, model A and model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $2.50, and the profit for each model B grate is $1.50. If 1,000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day, how many grates of each model should the division produce in order to help maximize the division's profits?
A) 120 model A, 160 model B; optimal profit $540
B) 200 model A, 160 model B; optimal profit $950
C) 0 model A, 250 model B; optimal profit $375
D) 200 model A, 0 model B; optimal profit $500

Question

Quizplus · Accepted Answer

The constraints given by the problem (1,000 lb of cast iron and 20 labor-hours available) and the requirements for each model (3 lb of cast iron and 6 min of labor for model A, 4 lb of cast iron and 3 min of labor for model B) fit best with option A, allowing for the production of 120 model A and 160 model B grates within the given resources, leading to the optimal profit of $540.

A Corporation Has a Division That Produces Two Models of Fireplace