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At HD Sport & Fitness gym, analysis shows that, as the demand of the gym, the number of members is 83 when annual membership fee is $17 per member and the number of members is 81 when annual membership fee is $24 per member. As the operator of the gym, you found out that number of members (q) and membership fee (p) have a linear relationship.

A) At what membership price, p, is the revenue maximized?
p=$??. Round your answer to 2 decimal places.

B) What is the maximum annual revenue?
R=$??. Round your answer to 2 decimal places.

Note: Round all coefficients of your revenue function to 2 decimal places.

Respuesta :

francocanacari

The price at which revenue is maximized is $ 157, and maximum annual revenue is $ 6751.

Since at HD Sport & Fitness gym, analysis shows that, as the demand of the gym, the number of members is 83 when annual membership fee is $ 17 per member and the number of members is 81 when annual membership fee is $ 24 per member, and the number of members and membership fee have a linear relationship, to determine at what membership price is the maximized revenue, and what is the maximum annual revenue, the following calculations must be performed:

  • 17 x 83 = 1411
  • 24 x 81 = 1944
  • 31 x 79 = 2449
  • 38 x 77 = 2926
  • 66 x 69 = 4554
  • 73 x 67 = 4891
  • 80 x 65 = 5200
  • 94 x 61 = 5734
  • 101 x 59 = 5959
  • 122 x 53 = 6466
  • 129 x 51 = 6579
  • 150 x 45 = 6750
  • 157 x 43 = 6751
  • 164 x 41 = 6724

Therefore, the price at which revenue is maximized is $ 157, and maximum annual revenue is $ 6751.

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