What Admission Price Should Be Charged In Order To Maximize Revenue And What Is The Maximum Revenue?
When a carnival owner charges $5.00 for admission, there is an average attendance of 100 people. For every $0.25 increase in the admission price, there is a loss of 2 customers from the average number. What admission price should be charged in order to maximize revenue and what is the maximum revenue?
Tags: Admission, Charged, Maximize, Maximum, Order, Price, Revenue, Should, What
So
if the price is $5.25, attendance is 98
if the price is $5.50, attendance is 96
etc.
Let the average attendance be denoted by q. Then q is related to the admission price p (in dollars) by
q = 100 – (p-5)/0.25
or after simplifying
q = 140 – 8p
Then the revenue R (in dollars) is the admission price, times the attendance:
R = pq = p(140 – 8p) = 140p – 8p²
I leave the rest to you.