(Solved): (24 point) Two routes connect a city and one of its suburban areas. During the peak-hour morning co ...

(24 point) Two routes connect a city and one of its suburban areas. During the peak-hour morning commute, a total 5,000 vehicles travel from the suburb to the city. Studies show the performance functions for these two routes are: Route 1: \( t_{1}=8+2 x_{1} \) Route 2: \( t_{2}=9+x_{2}^{2} \) \( t_{1} \) and \( t_{2} \) in minutes; \( x_{1} \) and \( x_{2} \) in thousands of vehicles per hour. (a) Determine the user-equilibrium travel time on each route? (8 points) (b) How many vehicle-hours can be saved from the user equilibrium travel condition if optimal system management is applied to these two routes? (8 points) (c) Assuming a road improvement project can change the link performance function of Route 2 into \( t_{2}=8+0.5 x_{2}{ }^{2} \), how much it can benefit the roadway traffic if the UE condition holds before and after the project? ( 8 points)