For a network with two alternative roads connecting A and B$,$ below figure shows the average travel time$-$based user equilibrium $($indicated by a triangle$)$ and marginal travel timebased system optimal $($indicated by a star$).$ The detailed outcomes of the user equilibrium and system optimal also show as below.

System Optimal Solution

$Q_1=2094$ veh$/$hr; $Q_2=3906$ veh$/$hr:

$t_1=41\mathrm{.}9$min,$t_2=61\mathrm{.}9$min

Total Travel Time $=329\mathrm{.}646$min

User Equilibrium Solution

$Q_1=2764$ veh $\frac{?}{hr}$;$Q_2=3236$ veh $\frac{?}{hr}$

$t_1=t_2=58\mathrm{.}2$min

Total Travel Time $=349,134$min

To drive the network from user equilibrium to system option, a toll will be imposed on one of the roads. On which road the toll should be imposed? Draw the average travel time curve of the road after imposing the toll. $(6$ points$)$

If the optimal toll is equivalent to $20$ minutes of travel time and the average value of time of travelers using the roadway system is $$30$ per hour, what is the dollar amount of the toll? $(2$ points$)$

For $5000$ travelers going from $A$ to $B,$ answer the following questions by comparing before and after imposing the toll,

a$.$ After imposing the toll, how many travelers switch from Road $1$ to Road $2?(1$ point$)$

b$.$ For switched travelers, what is the increased travel time that they spend for going from $A$ to $B?(1$ point$)$

c$.$ For travelers taking Road $2,$ what is the travel time difference before and after imposing the toll? $(1$ point$)$

d$.$ What is the monetary value of total increased travel time of travelers taking Road $2?(1$ points$)$

e$.$ How many travelers continue staying on Road $1$ after imposing the toll? $(1$ point$)$

f$.$ For those stayed on Road $1,$ how much travel time each travers can save? $(1$ point$)$

g$.$ What is the total saved travel time of travelers taking Road $1?(1$ point$)$

h$.$ What is the monetary value of saved travel time? $(1$ point$)$

i$.$ What is the saved travel time of all travelers? $(1$ points$)$

j$.$ What is the monetary value of saved travel time? $(1$ point$)$

$k.$ What is the revenue collected from imposing the toll? Number $3$No