+73 The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function p(t) = -16t^2 + 800t - 4000 where t is the price of each ticket.
a. What ticket price would give the maximum profit?
b. What is the maximum profit?
c. What ticket price would give the profit of $5424?
5424 = -16t^2 + 800t - 4000
+128474 p(t) = -16t^2 + 800t - 4000
a) The price of the ticket that maximizes the profit is given by :
-800 / ( 2 * -16 ) = -800 / (-32) = $25
b) The max profit is -16(25)^2 + 800(25) - 4000 = $6000
c) 5424 = -16t^2 + 800t - 4000 subtract 5424 from each side
-16t^2 + 800t - 9424 = 0 multiply through by -1
16t^2 - 800t + 9424 = 0 divide through by 16
t^2 - 50t + 589 = 0 factor as
(t - 31) (t - 19) = 0
Setting both factors to 0 and solving for t produces two possible prices...$19 or $31
