Question

Demand for tickets to a soccer game is given by q(p)=-7.4p^(2)+492.9p+10,000. What price will maximize revenue?

Answer 1

Revenue maximizes at prices p=52.91

Step-by-step explanation:

Given:

q(p) = −7.4p^2 + 492.9p + 10,000

Revenue function is

R(p) = p × q

R(p) = p (−7.4p^2 + 492.9p +10,000)

R(p) =−22.2p^2 + 985.8p + 10,000

For maximizing revenue

R(p) = 0

P =−8.51, 52.91

R(p) = −44.4p + 985.8

R″(p) < 0,

P = 52.91

Revenue maximizes at prices p=52.91