Please see the question below:

2. Consider the market for gasoline in a small town where all the 100 residents live at equal distances on a mile-long stretch of Main St. There are two gas stations, Edna's and Murphy's, that are located on opposite ends of town; assume that Edna's is located on the west side and Murphy's on the east side. All residents need only 1 gallon of gas. The gas at Edna's is of a better quality than Murphy's. As a result, each resident values a gallon of gas bought from Edna's at VE = $4, and a gallon of gas bought from Murphy's at VM = $3. Assume that both gas stations have a marginal cost of 0 for gas production. Fixed costs are also 0. Each consumer experiences a transportation cost of $0.5 (50 cents) per round-trip mile. Suppose that Edna and Murphy's set prices sequentially, with Edna choosing her price first. a. If Edna set a price of PE, and Murphy set a price of PM, what would be the location, *m, of the customer who was just indifferent between buying gas from either gas station? b. What would be the total demand for gas at each station as a function of prices, DE(PE, PM) and DM (PE, PM), and the corresponding profits TE (PE, PM) and IM(PE. PM)? c. If Murphy observes Edna set a price of PM, what price should Murphy set? Show your work. d. Given the answer in part (c), what equation does Edna need to solve to determine her optimal price PE