Question

A community theater uses the function p(d)=−4d2+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. 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. At what price would the theater make the maximum profit, and what is that maximum profit. Show your reasoning.

Answer 1

price = $25

maximum profit is $2400

Explanation:

Given the function modeled by the community theatre as

p(d)=−4d^2+200d−100

The maximum profit will be ,ade at dP/dd = 0

dP/dd = -8d + 200

0 = -8d + 200

8d = 200

d = 200/8

d = 25

hence he theatre will make maximum profit at a price of $25

Substitute d = 25 to get the maximum profit

p(25)=−4(25)^2+200(25)−100

p(25) = -2500+5000-100

p(25) = 2400

Hence the maximum profit is $2400