Help with microeconomics question

Consider a beach of length 1. Consumers are evenly (uniformly) distributed along the beach and dislike walking in the hot sand. There are two ice cream stands. (a) What is the location of the stands in equilibrium if prices are fixed exogenously (and cover the expenses)? You must prove your answer. (7 Marks) (b) Now suppose that the first stand is fixed at point zero. Prices are still fixed exoge- nously. What location will the second stand choose? (6 Marks) (c) Consider the full game, where stands first choose a location and then a price. How would you solve this game (just a sketch of the steps needed)? (7 Marks) (d) Now solve the full game (that is, find prices and locations), assuming that the first stand is fixed at point zero, production costs are zero and walking cost is quadratic, meaning that when a consumer walks the distance 3:, the cost is 2:2. You are allowed to use the fact that with quadratic costs the strategic effect of a change in location towards the competitor dominates the demand effect (i.e. profits fall when you move closer to your competitor). Are the locations you get the same as in part (b)? Why? What would profits be if locations were the same as in part (b)? (10 Marks) (e) Does the full game have an equilibrium if prices and locations are endogenous and walking costs are linear? Provide some intuition, in no more than five short sentences