Route Choice$/$Traffic Assignment

$(25$ points$)$ Highway performance functions have been developed based on data

collected from travel time studies on each of two available routes

$t_1,t_2=$ average travel times on routes $1$ and $2$ in minutes and

$x_1,x_2=$ traffic flow on routes $1$ and $2$ in $1000$ s of vehicles$/$hour

The hourly flow rate is $5000$ veh$/$hr$.$

Under user equilibrium conditions and system optimization, determine:

Travel times on each route

Traffic volumes on each route

Total system travel time