Question

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 $1000$ fewer tickets a week. how many dollars should they charge to maximize their total revenue?

Answer 1

Suppose GetThere Airlines increases their ticket price to $200+10n = 10(20+n)$ dollars. Then the number of tickets they sell is $40,000-1000n = 1000(40-n)$ . Therefore, their total revenue is

$$10(20+n)\cdot 1000(40-n) = 10000(20+n)(40-n) = 10000(800+20n-n^2).$$

This is maximized when $n=-\left(\frac{20}{2\cdot(-1)}\right)=10$ . Therefore, they should charge $200+10\cdot 10 = \boxed{300}$ dollars per ticket.