Question

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 6 clients. how much should the club charge each month to optimize the revenue from monthly​ dues?

Answer 1

$180.83

Step-by-step explanation:

number of clients = 1900

charge per client = $45

increase by $1 leads to loss of 6 clients

let the increase in charge be represented as : X

loss of clients = 6X

therefore revenue generated ( Rx) = ( $45 + X ) (1900 - 6X) = ( 45 * 1900 - 45(6X) + 1900X - 6
`x^(2)`)

= 85500 - 270X + 1900X - 6
`x^(2)`

R(x) = - 6
`x^(2)` + 1630 x + 85500

find x =
`(-b)/(2a)` =
`(-1630)/(2(-6)) = (-1630)/(-12)` = 135.83

to optimize the revenue from monthly dues will be

charge per client + X = $45 + $135.83 = $180.83