Please help with question below:

Consider a spatial (Hotelling) model of product differentiation. There is a customer at each point of the segment on the interval [0,20]. Their location on this|interva| is their taste x. A customer with taste x who pays 'p for the product from the firm located at 3! gets a utility of 40 2|x y| p, and there is always an option of not buying a product at all, which gives a utility of 0. Suppose that there are two firms that produce two kinds of a product. Firm A produces the good that corresponds to taste of 0, and firm B produces the good that corresponds to the taste of 10. U=402|xy|p Note: for all problems below, we assume Total Cost = Marginal Cost = 0 (a) Assume that firms A and B both set a price equal to 6. Which consumer is indifferent between buying from firm A and not buying anything? Which consumers don't buy anything? What is the profit of each firm? (b) Now suppose that the prices are pA and 193, respectively. Which customer (defined by taste x} is indifferent between buying from Firm A and B? Find x as a function ofthe two firms' prices. Are all customers buying the product