# If a gym charges its members $300 per to join, they get 1000 members. For each$2 increase in price they can expect to lose 5 members. How much should the gym charge to maximize its revenue?

##### 1 Answer
Apr 28, 2018

Gym charge should be  $350 from $875$members to get maximum revenue of $306250

#### Explanation:

Gym charge is C= $300 and number of members are $M = 1000$Revenue is R= C* M =$300000 . Let the number of $2 increase be $x$then revenue is $R = \left(300 + 2 x\right) \cdot \left(1000 - 5 x\right)$$R = - 10 {x}^{2} + 2000 x - 1500 x + 300000$or $R = - 10 {x}^{2} + 500 x + 300000$or $R = - 10 \left({x}^{2} - 50 x\right) + 300000$or $R = - 10 \left({x}^{2} - 50 x + 625\right) + 6250 + 300000$or R = -10( x-25)^2 + 306250 ; R  will be maximum when x-25=0 :. x=25 :. 2 x=50 ; C=300+50=350 ; $M = 1000 - 5 \cdot 25 = 875 , R = 306250$and so gym charge should be $350 from $875$ members to get maximum

revenue or \$306250 [Ans]