Pre calc World prob

Question

A baseball team plays in a stadium that holds 68000 spectators. With the ticket price at $10 the average attendance has been 29000. When the price dropped to $8, the average attendance rose to 34000. Assume that attendance is linearly related to ticket price.

What ticket price would maximize revenue? $

Answer 1

For every $2 decrease in price the attendance increase by 500.

R(p) = (2900 + 500p)(10 - 2p), where p represents each decrease of $2.

Multiply out and determine p for a maximum.