The Portland Sea Dogs, the AA affiliate of the Boston Red Sox major league baseball team, have enjoyed a surge in popularity. During a recent home stand, suppose the club offered $5 off the $12 regular price of reserved seats, and sales spurted from 3,200 to 5,200 tickets per game.

A. Derive the function that describes the price/output relation with price expressed as a function of quantity (tickets sold). Also express tickets sold as a function of price.

B. Use the information derived in part A to calculate total revenues at prices in $1 increments from $5 to $15 per ticket. What is the revenue-maximizing ticket price? If variable costs are negligible, is this amount also the profit-maximizing ticket price?