Question

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.

Answer 1

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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