+981 Usher fairs currently charges 200 dollars per entry ticket and sells 40,000 entry 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?
+128407 Let x be the number of $10 increases
Tickets sold * Price = Revenue
We have this
(40000 - 800x) ( 200 + 10x) = Revenue simplify
40000(200) - (800 * 200)x + ( 40000*10)x + 8000x^2 = Revenue
8000000 - 160000x + 400000x - 8000x^2 = Revenue
R = -8000x^2 + 240000x + 8000000
To maximize the revenue....the number of $10 increases = x = -240000/(-2 * -8000) = 15
So....the price of a ticket that maxes the revenue = (200 + 15*10) = 200 + 150 = $350
