A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $9 the average attendence has been 25000. When the price dropped to $7, the average attendence rose to 29000.

Question

Assume that attendence is linearly related to ticket price.

What ticket price would maximize revenue?

Answer 1

slope = (25 - 29)/(9 - 7) = -2

-2 = (A - 29)/(P -7)

-2P + 14 = A - 29

A = 43 - 2P

Revenue = A * P = 43P - 2P

Now compute the derivative of revenue with respect to price and set it = to 0.

Solve for P which will be the price to maximize revenue.