As manager of Citywide Racquet Club, you must determine the best price to charge for locker rentals. Assume that the (marginal) cost of providing lockers is 0. The monthly demand for lockers is estimated to be Q = 100 - 2P where P is the monthly rental price and Q is the number of lockers rented per month. What price would you charge? How many lockers are rented monthly at this price? Explain why you chose this price.

Answer 1

You want to maximize income which is P*Q
P Q = 100 P - 2 P ^2

2 p^2 -100 p = - income
where is that derivative = 0?
4 p - 100
p = 25 seems to be it.
then you rent
Q = 100 - 50 = 50 of them
and you make
PQ = $1250
If you have not had calculus, find the vertex of that parabola by completing the square