4. There are two cities A and B joined by routes depicted in Figure 1. There are 80 60 104y A. 10+x 60 Figure 1: Traffic goes from start A to destination B. travelers who begin in A and must travel to B. The variables r and y denote the numbers of travelers using the respective road between its endpoints. The times are given for each edge in minutes per traveler. Nash equilibria are determined subject to the assumption that the travelers simultaneously choose which route to use. The social cost of traffic is understood as the sum of travel times over all the travelers. (a) Consider first this network as it was before direct connections between C and D of no travel time were built. Find the Nash equilibrium. (b) Consider this network with direct connections between C and D of no travel time available, as in Figure 1. Find the Nash equilibrium. What happens to the total travel time as a result of the availability of the new roads, comparing to the traffic in Nash equilibrium in (a)? (c) Suppose you could assign travelers to the routes depicted in Figure 1. Propose an assignment of routes that reduces the social cost of traffic relative to what it was in Nash equilibrium in part (a)