Exercise 5: Dividing the Market Suppose there are two producers (U1 and U2), each of them producing a different product, and two retailers (R1 and R2). R1 only sells product 1 and R2 only sells product 2. The market is divided in two territories (zones): at and 19. Both retailers operate in both zones. In zone k, market demand for product 1 is given by D1 = \"[5 7 pm + dek] and for product 2 is D2 = \"[5 F m + dplk], for k = (1, b, with 04,, + och = 1. For a retailer operating in zone It, cost function is given by the price it must pay for each unit sold (an for retailer 1 and W2 for retailer 2), plus a transportation cost of tk for each unit sold. That is: C,- = (w, + tq for retailer 1' selling in zone It. As for the producers, the rst one has a unitary cost of cl > 0 while for the second one we have C2 > 0 Inwhat follows, assume: 5! 1, ta 1, t5, 2, ma sq, , 61 0.8 and C1 = 1.4. NIrI a) (8 points) Set up and solve both retailer's problems at each zone. Find all four retail prices ( pm, p2\