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

Answer:

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]