Question

QUICK!!!! A community theater uses the function p(d)=−4d^2+200d−100 to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at d dollars each. A. Write and solve an equation to find out the prices at which the theater would earn $1,500 in profit from the comedy show each weekend. Show your reasoning. B. At what price would the theater make the maximum profit? C. what is that maximum profit?

Answer 1

A. -4d² + 200d - 100 = 1,500

-4d² + 200d - 1,600 = 0

4d² - 200d + 1,600 = 0

d² - 50d + 400 = 0

(d - 10)(d - 40) = 0

d = $10, $40

B. p'(d) = -8d + 200 = 0

8d - 200 = 0

8d = 200

d = $25

C. p(25) = -4(25²) + 200(25) - 100

= -4(625) + 5,000 - 100

= -2,500 + 5,000 - 100

= $2,400