SOLUTION: A health club currently charges its 2,000 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 980573: A health club currently charges its 2,000 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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A health club currently charges its 2,000 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.
:
let x = no. of $1 increases in dues and no. of 7 client losses
:
Write a revenue equation; Rev = monthly charge * no. of clients
R(x) = (44 + x)*(2000-7x)
FOIL
R(x) = 88000 - 308x + 2000x - 7x^2
R(x) = -7x^2 + 1692x + 88000
A quadratic equation; the max will be at the axis of symmetry x = -b/(2a)
x = %28-1692%29%2F%282%2A-7%29
x = %28-1692%29%2F%28-14%29
x = $120.86 increase; 44 + 120.86 = $164.86 a month dues for max revenue
:
That seem unrealistic, but there it is.