SOLUTION: A health club currently charges its 1900 clients monthly membership dues of $45. The board of directors decides to increase the monthly membership dues. Market research shows that

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Question 1097010: A health club currently charges its 1900 clients monthly membership dues of $45. 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 3 clients. How much should the club charge each month to optimize the revenue from monthly dues?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A health club currently charges its 1900 clients monthly membership dues of $45.
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 3 clients.
How much should the club charge each month to optimize the revenue from monthly dues?
:
let x = no. of $1 increases, and -3x = the no. of client decreases
Revenue = price * no. of clients
R(x) = (45 + x)(1900 - 3x)
FOIL
R(x) = 85500 - 135x + 1900x - 3x^2
a quadratic equation
y = -3x^2 + 1765x + 8550
The max y (revenue) occurs on the axis of symmetry. x = -b/(2a)
x =
x = 294
Max revenue occurs when 294 + 45 = $339 a month are the dues
then the no. of clients: 1900 - 3(294) = 1018 clients
:
:
Not a realistic scenario!