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# The profit from selling local ballet tickets depends on the ticket price. Please Help!

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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

Apr 10, 2018

### 1+0 Answers

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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   Apr 10, 2018