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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 7,000 fewer tickets a week. How many dollars should they charge to maximize their total revenue?

 Jan 31, 2021
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x = number of 10 dollar increases

then

revenue =( 40000-7000x)(200 + 10x)

             = 8 000 000 + 400,000x  -1,400,000x - 70,000x^2

             -70 x^2 -1000x +8000

 

max occurs at x = -b/2a

                         =  - -1000/ (-140)= -7.14           -7.14   ten dollar increases is  -71.40185.70

 

200 -71.40= 128.60    price for max rev      (this assumes a $10 DECREASE will result in 7000 MORE seats sold)

 

so any further increase in tix price will result in LOWER revenue !!!!      SO they are at max revenue (unless they LOWER prices)

 Jan 31, 2021

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