Consider the demand for tickets to see a specific hockey team play. The price of the ticket can be related to the quantity demanded (q) by the function: . When the arena is not close to full capacity the total cost can be expressed by the function: .

Find marginal revenue (MR) as a function of quantity demanded.

Let and be the price and quantity demanded where profit is maximized.
 

The hockey players union has negotiated a deal requiring the team owner to pay an extra $1,000,000 a year in salaries to the players. What should the new ticket price () be to ensure that profit is maximized.

You can earn partial credit on this problem.