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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?

 May 16, 2020
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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.

 May 16, 2020

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