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.
:
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 = {{{(-1692)/(2*-7)}}}
x = {{{(-1692)/(-14)}}}
x = $120.86 increase; 44 + 120.86 = $164.86 a month dues for max revenue
:
That seem unrealistic, but there it is.