posted by Andrew .
An auditorium has 1600 seats. At a ticket price of $6, the owners can sell 1200 tickets. For each 25 cent increase in price the tickets sold reduces by 25. What price should the owners set to maximize the income?
let the number of 25 cent increases by x
income = ticket price x number of tickets sold
income = (6+.25x)(1200-25x)
= 7200 - 150x + 300x - 6.25x^2
= -6.25x^2 150x + 7200
d(income)/dx = -12.5x + 150 = 0 for a max of income
12.5x = 150
x = 12
so the price for max income should be 6 + .25(12) = $9.00