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= (300+2 x)* (1000-5 x)

R = -10 x^2 +2000 x - 1500 x + 300000 or

R = -10 x^2 +500 x + 300000 or

R = -10( x^2 -50 x ) + 300000 or

R = -10( x^2 -50 x +625 )+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*25=875 , R=306250 and so gym charge

should be $350 from 875 members to get maximum

revenue or $306250 [Ans]