Consider the Utica Slappers, a hockey team that plays in an arena with 8,000 seats. The only cost associated with staging a hockey game is a fixed cost of $6,000: The team incurs this cost regardless of how many people attend a game. The demand curve for hockey tickets has a slope of $0.001 per ticket ($1 divided by 1,000 tickets):Each $1 increase in price decreases the number of tickets sold by 1,000. For example, here are some combinations of price and quantity:Price per ticket $4$5$6$7......Quantity of tickets 8,0007,0006,0005,000.

The owner's objective is to maximize the profit per hockey game (total revenue minus the $6,000 fixed cost).a. What price will maximize profit? b. If the owner picks the price that maximizes profit, how many seats in the arena will be empty? c. Is it rational to leave some seats empty?