GetThere Airlines currently charges 200 dollars per ticket and sells 40,000 tickets a week. For every 10 dollars they increase the ticket price, they sell 800 fewer tickets a week. How many dollars should they charge to maximize their total revenue?
Suppose GetThere Airlines increases their ticket price to 200+10n = 10(20+n) dollars. Then the number of tickets they sell is 40,000-1000n = 800(40-n) . Therefore, their total revenue is
10(20+n)\cdot 800(40-n) = 8000(20+n)(40-n) = 8000(800+40n-n^2).
This is maximized when n=-(\frac{40}{2\cdot(-1)})=20 . Therefore, they should charge 200+20\cdot 10 = 400 dollars per ticket.