Please help with the following homework problem from a game theory in economics class. It is a Hotelling Model problem.

Two carts selling coconut milk are located at 0 and 1, 1 mile apart on Copacabana beach in Rio de Janeiro. The carts Cart 0 and Cart 1 charge prices p0 and 191 for each coconut. The cost of each coconut milk is assumed to be zero. One thousand beach goers buy coconut milk, and these customers are uniformly distributed along the beach between the two carts. Each beachgoer will purchase one coconut milk per day and get a utility of u from consuming it. Assume u is high enough so that everyone is willing to walk as far as they have to. In addition to the price, each will incur a transportation cost of 0.6d2, where d is distance in miles from her beach blanket to the coconut cart. Beachgoers will not bring coconut milk for their friends if they are going to get it for themselves. (a) Find the beachgoer a: that is indifferent between going to Cart 0 or Cart 1, given the prices p0 and p1. (b) Given your answer in part (a), what are the individual demand functions for the two carts? What are the two prot functions? (c) Find the best responses of each cart as a function of their rival's price. What is the purestrategy Nash equilibrium of this game