Question

A hockey team plays in an area with seating capacity of 15,000 spectators. with the ticket price set at 12 “dollars”, average attendance at recent games has been 11,000. A market survey indicates that for each dollar the ticket price is lowered, the average attendance will increase by 1000. What price should the owners of the team set as the ticket price to maximize their revenue from the ticket sales?

Answer 1

$R=(12-x)(11000+1000x)=-1000x^2+1000x-132000\\ \frac{dR}{dx}=-2000x+1000\\ \frac{dR}{dt}=0\to -2000x+1000=0\to x=0.5$

$12-x=12-0.5=\$11.5$

The owners of the team should set $11.50 as the ticket price to maximize their revenue from the ticket sales.