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?
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