Please answer both parts and provide a diagram.

You’re the manager for a college football team. Assume you own the stadium and the variable cost per attendant is $0. You’ve been told by your in-house economist that you should set the price of tickets at $50 to maximize profit (at current, you set one price). Your football coach is really pushing to sell out the game.

1. Under what condition will profit maximization also result in a sold out game? Under what condition will profit maximization not result in a sold out game? (Solving mathematically and drawing a figure would be helpful).

2. If the game is not sold out at the profit maximizing price, what strategy could the team employ that would result in a lower deadweight loss?