Figure 2-1 shows a transportation network with give links and two O-D pairs: 12 and 32. The O-D demands are: 1-2: 3-2: 20 units/hour 60 units/hour and the link travel time functions are f =1+0.15(x/a), where a is the link's number shown in the figure. 3 2 5 3 4 Figure Q2-1. The network structure for Question 6 (a) Build a convex programming model for the deterministic user equilibrium (DUE) traffic assignment of the transportation network by explicitly defining paths, and demonstrate the optimal solution of the convex programming fulfils the DUE conditions by using the KKT conditions. (b) Build a convex programming model for the logit-based stochastic user equilibrium (SUE) traffic assignment of the transportation network by explicitly defining paths, and demonstrate the optimal solution of the convex programming fulfils the logit- based SUE conditions by using the KKT conditions. (c) Show your working (i.e., step-by-step procedure) to find the DUE link flow solution and DUE travel time between each OD pair by using the Frank-Wolfe method. You can choose an appropriate stop criterion for the Frank-Wolfe method. (d) Show your working (i.e., step-by-step procedure) to find the logit-based SUE link flow solution by using the MSA method. You can choose an appropriate stop criterion for the MSA method. It is assumed that = 0.1 for the logit-based SUE traffic assignment