Assume a Hotelling line of a distance l = 1. There are two companies A and B, both of them being located at a longer distance. Company A is placed closer to the end of the line, while company B is placed further away. The distance from the beginning of the line to company A is a (a > l) and to B is b (with b > a > l). Assume also that an indifferent consumer is located close to the beginning and the distances to A and B are, x and y respectively, where y = x + b a. Assume quadratic transportation costs, i.e. cx2 and cy2, and prices PA and PB. Find the equilibrium prices and the condition under which both firms will have positive sales. (Hint: Assume that the quantity demanded of firm A is qA = a x, qB = 1 - (a x) & use the following parameters: c = 1, a = 1.2).