How many sets of each model should be manufactured per day to maximize the profit?

Question

A manufacturer of golf clubs makes a profit of $50 per set on a model A set and $55 per set on a model B set. Daily production of the model A clubs is between 20 and 50 sets, inclusive, and that of the model B clubs is between 10 and 30 sets, inclusive. The total daily production is not to exceed 50 sets. How many sets of each model should be manufactured per day to maximize the profit?

Answer 1

Let A=number of Model A manufactured daily. Let B=number of Model B manufactured daily.

Profit = 50A+55B

A+B=50

A=50-B Profit = 50(50-B)+55B = 2500-50B+50B = 2,500+5B is at a maximum by maximizing B at 30.

B=50-A Profit = 50A +55(50-A) = 50A+2750-55A = 2,750-5A is at a maximum by minimizing A at 20

you do as many Model B as possible, which is 30. That means A=20 is the maximum possible for Model A.

Maximum profit is 50(20)+55(30)= 1,000+1,650=$2,650

You want maximum number of B possible because it is more profitable.