A manufacturer of tennis rackets makes a profit of $15 on each oversized racket and $8 on each standard racket. To meet dealer demand, daily production of standard rackets should be between 30 and 80, and production of oversized rackets should be between 10 and 30. 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 profit?

Question

Mathematics

Dereon Esparza

22 July, 13:11

A manufacturer of tennis rackets makes a profit of $15 on each oversized racket and $8 on each standard racket. To meet dealer demand, daily production of standard rackets should be between 30 and 80, and production of oversized rackets should be between 10 and 30. 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 profit?

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Kaeden Cohen · Answer 1

30 oversized rackets and 50 standard rackets

Step-by-step explanation:

To maximize profit, it is very essential she strikes a balance between the two type of rackets. It is important to note that the profit on oversized racket is twice that of standard racket. Hence, she must make as many oversized rackets as possible.

The highest number of oversized racket she can make is 30. Subtracting 30 from the total number of rackets give 50 standard racket