SOLUTION: A health club currently charges its 1800 clients monthly membership dues of $44. The board of directors decides to increase the monthly membership dues. Market research shows that
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Question 921247: A health club currently charges its 1800 clients monthly membership dues of $44. The board of directors decides to increase the monthly membership dues. Market research shows that each $1 increase in dues will result in the loss of 7 clients. How much should the club charge each month to optimize the revenue from monthly dues? Round to the nearest cent.
You can put this solution on YOUR website! A health club currently charges its 1800 clients monthly membership dues of $44. The board of directors decides to increase the monthly membership dues. Market research shows that each $1 increase in dues will result in the loss of 7 clients. How much should the club charge each month to optimize the revenue from monthly dues? Round to the nearest cent.
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Revenue = Unit price*Number of clients
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R(x) = (44+x)(1800-7x)
R(x) = -7x^2 + 1492x + 79200
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Max occurs when x = -b/(2a) = -1492/(-14) = 106.57
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Ans: They should charge 44+106.57 = $150.57
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Cheers,
Stan H.
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