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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?

 Jun 10, 2021
 #1
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This question has been asked multiple times.....it is messy because of the big numbers involved, but it looks like this:

(40 000 - 400x)(200 + 10x)  = revenue        Where x is the number of 10 dollar increases

 

= -4000 x^2  + 320 000 x + 8 000 000

 

This is a quadratic that is a dome shaped parabola with the max occuring at    -b/2a  = 40       ten dollar increases

    which means a ticket price of 600 dollars

 Jun 10, 2021

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