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An Ariline currently charges 200 dollars per ticket and sells 40,000 tickets a week. For every 10 dollars they increase the ticket price, they sell 400 fewer tickets a week. How many dollars should they charge to maximize their total revenue?

 Dec 28, 2021
 #1
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The airlines should charge 180 dollars per ticket.

 Dec 28, 2021
 #2
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x = # 10 dollar increases       (40 000 - 400x)    will be # tix sold  at price $ ( 200+ 10x)

 

revenue =   (40 000 - 400x)(200 + 10x)

                         8 000 000  + 400,000x   - 80,000x - 4 000x^2 

                         - 4000 x^2 + 320 000x + 8 000 000                    Max occurs at x = - b/2a = -320 000 / (2*(-4000)) = 40  

 

40 ten dollar increases   means price should be 600 dollars     and   24 000 tickets will be sold               

 Dec 28, 2021

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