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?
:
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 = {{{(-1765)/(2*-3)}}}
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!