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

 Aug 1, 2021
 #1
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# of ten dollar increase in tix price = x

 

revenue =  (40 000 - 100x)(200 + 10x)

                   ( 8 000 000 + 400 000x - 20 000x - 10 000x^2 )    

                    (-10 000 x^2 + 380 000 x + 8 000 000)          this is a dome shaped parabola (due to the negative coefficient for x^2)

                               max will occur at x = -b/2a     =   380 000/ (10 000(2)) = 19  

 

19 ten dollar increases will make ticket price = 200 + 190 = 390 dollars

 Aug 1, 2021

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