SOLUTION: I will give it another shot. Gold's Gym charges $300 per year for new members to join, they get 1000 members. The gym can expect to lose about 5 members for the $2.00 increase in p

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Question 894595: I will give it another shot. Gold's Gym charges $300 per year for new members to join, they get 1000 members. The gym can expect to lose about 5 members for the $2.00 increase in price. How much should the gym charge to maximize its revenue? What is Gold's Gym maximum revenue?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
q for how many members
x for price

PRICE__________Members
300____________1000
302____________1000-5
304____________1000-10
.
highlight_green%28q=300-%285%2F2%29x%29. Member count is a function of price.

Let r stand for revenue.
r=q%2Ax
r=x%28300-%285%2F2%29x%29
or in general form for the function,
highlight_green%28r=-%285%2F2%29x%5E2%2B300x%29

You want the maximum of this formula for r, the vertex. Find the roots, check the value at the midpoint of the two roots and use it to compute r.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

I will give it another shot. Gold's Gym charges $300 per year for new members to join, they get 1000 members. The gym can expect to lose about 5 members for the $2.00 increase in price. How much should the gym charge to maximize its revenue? What is Gold's Gym maximum revenue?


Per-year charge:          $highlight_green%28350%29

Per-year maximum revenue: $highlight_green%28306250%29