A manufacturer of tennis rackets makes a profit of $16 on each oversized racket and $10 on each standard racket. To meet dealer demand, daily production of standard rackets should be between 25 and 80, and production of oversized rackets should be between 8 and 33. To maintain high quality, the total number of rackets produced should not exceed 80 per day. How many of each type should be manufactured daily to maximize the profit?

Question

Quizplus · Accepted Answer

To maximize profit, the manufacturer should produce the maximum number of the most profitable item (oversized rackets at $16 profit each) without exceeding production limits. The maximum for oversized rackets is 33. With a total production limit of 80 rackets per day, this leaves room for 47 standard rackets (80 - 33 = 47), which is within the production limit for standard rackets (25 to 80). This combination maximizes profit while adhering to all constraints.

A Manufacturer of Tennis Rackets Makes a Profit of $16