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?

$180.83

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)

                                                          = 85500 - 270X + 1900X - 6

R(x) = - 6 + 1630 x  + 85500

find x = = = 135.83

to optimize the revenue from monthly dues will be

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