There are two cities A and B joined by two routes. There are 80 travelers who begin in city A and must travel to cith B. There are two routes between A and B. Route I begins with a highway leacing city A, this highway takes one hour of travel time regardless of how many travelers use it, and ends with a local street leading into city B. This local street near city B requires a travel time in minutes equal to 10 plus the number of travelers who use the street. Route II begins with a local street leaving city A, which requires a travel time in minutes equal to 10 plus the number of travelers who use this street, and ends with a highway into city B which requires one hour of travel time regardless of the number of travelers who use this highway. (a) Draw the network described above and label the edges with the travel time needed to move along the edge. Let r be the number of travelers who use Route I. The network should be a directed graph as all rouds are one-way. (b) Travelers simultaneously choose which route to use. Find the Nash equilibrium value of r. (c) Now the government builds a new (two-way) road connecting the nodes where local streets and highways meet. This adds two new routes. One new route consists of the local street leacing city A (on Route Il), the new road and the local street into city B (on Route 1). The second new route consists of the highway leaving city A (on Route 1), the new road and the highway leading into city B (on Route II). The new road is very short and takes no travel time. Finde the new Nash equilibrium