<PRE><B>Question 906178</B>
A health club currently charges its 2,000 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 7 clients.
 How much should the club charge each month to optimize the revenue from monthly dues? 
:
let x = no. or dollar increases
and
7x = no. clients lost
:
Rev = f(x)
f(x) = (45 + x) * (2000-7x)
FOIL
f(x) = 90000 - 315x + 2000x - 7x^2
f(x) = 90000 + 1685x - 7x^2
As quadratic equation where a = -7 and b = 1685 the axis of symmetry will give the max revenue x = -b/(2a)
x = {{{(1685)/(2*-7)}}}
x = +120.357 ~ 120
:
Max revenue when: 120 + 45 = $165 a month with
2000 - 7(120) = 842 clients
Rev then: 842 * 165 = $138,930

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