5. (26%) Consider a town with a single street of 1 km long with 3,000 people spread uniformly along it. Two stores, 1 and 2, are located at the opposite ends of the street and sell the same product (store 1 is located at the left end). The cost of walking is tI = $6 per km to store I and t2 = $9 per km to store 2 for each consumer. The net utility of a consumer located at point x from buying a product at store 1 is 1M1) = 100 p1 t1x, where p,- is a price of the product at store 1' = 1,2. The net utiJity from buying at store 2 is light) = 100 p2 tzu :.r). The average cost of the product for each store is c = 4. (a) Assume that all consumers bu],r product from the sellers. Find the demand functions Dit'pypz) and the prot functions mt :11.sz for each store 1' = 1,2 as flmcu'ons of prices mpg. (b) Find the equilibrium prices