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 800 fewer tickets a week. How many dollars should they charge to maximize their total revenue?
We want to maximize the quadratic (40000 - 800n)(200 + 10n), which expands as -8000n^2 + 200000n + 8000000. The maximum occurs at n = 25/2, so they should charge 200 + 10*25/2 = 325.