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?
x = # 10 dollar increases (40 000 - 400x) will be # tix sold at price $ ( 200+ 10x)
revenue = (40 000 - 400x)(200 + 10x)
8 000 000 + 400,000x - 80,000x - 4 000x^2
- 4000 x^2 + 320 000x + 8 000 000 Max occurs at x = - b/2a = -320 000 / (2*(-4000)) = 40
40 ten dollar increases means price should be 600 dollars and 24 000 tickets will be sold
