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?
revenue = (40 000 - 100x)(200 + 10x) where x = the number of 10 dollar inreases
revenue = - 1000x^2 + 380 000 x + 8 000 000 simplify a bit (to make it easier to work)
- x^2 + 380 x + 8000
Max will be at - b/2a = - 380 /(2(-1)) = 190 = x
190 x 10 = 1900 increase 1900 + 200 = 2100 dollars for max revenue (Yikes! That doesn't seem correct....check my math!)
