Suppose there are two airlines, each one runs one flight a day to Chicago. Delta runs one at 8AM and United runs one at 6PM. There are 100 people whose preferences are evenly distributed between 8AM and 6PM. Each consumer values the flight at $300, but dislikes leaving at a different time then their preferred time by $0.5 per minute. The marginal cost to add a consumer is $20. To make things easier, normalize 8AM to location 0 and 6PM at location 600 (600 minutes from 8AM). Assume that all consumers will want to buy a plane ticket.

(a) Find the demand function for each firm.
(b) Write down the profit function for each firm.
(c) Find the best response function for each firm.
(d) Find equilibrium prices, number of passengers, and profits for each firm.