Consider the following routing game with two routes where l,12 are the travel times on each route when the fraction of traffic on each route is given by and 22. The parameters a, b satisfy a > 0 and 0 b 1. See Figure 1. (a) Find the optimal routing [3 pt.] (b) Find the equilibrium routing [3 pt.] (c) Suppose everyone values saving an hour of time at $10/hour. What tax and on which route will result in the optimal routing as an equilibrium? [3 pt.] (d) What is the maximum ratio of inefficiency of the travel time under equilibrium routing relative to the optimal routing ( AvgTime Equi) [1 pt.] AvgTime Opt