2. Let's go back to Tuftsville (see Chapter 10), where everyone lives on Main Street which is ten miles long. 1,000 people are evenly distributed on Main Street and every day they buy a fruit smoothie from one of the two stores located at either end of Main Street. Customers use their motor scooters to and from the store. A motor scooter uses gas at $0.50 per mile. Customers purchase a smoothie from the store that has the lowest price of the store's smoothie price plus the travel cost the customer pays to get to the store. Ben owns the store at the west end of Main Street and Will owns the store at the east end of Main Street. The marginal cost of the smoothie is constant and is SI for both Ben and Will. In addition, the two each pay Tuftsville $250 a day for the right to sell the smoothie.

a. Ben sets his price first, followed by Will who sets his price. After the prices are offered, customers purchase the fruit smoothie from the store offering the lowest price, including travel costs for their scooter. How much do Ben and Will charge each?

b. How many customers does each store get, and what is the profit for each store?