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?
+37146 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
