Consider the following transportation network with a single O$/$D pair $w=(x,y)$ and $2$ links.

The user link cost functions are given by:

$c_a(f_a)=f_a+25,c_b(f_b)=f_b+20$

and the travel disutility function is: ${}_w(d_w)=-d_w+45.$

$($a$).$ Reformulate the elastic demand traffic network equilibrium problem as a fixed demand problem

using the excess overflow reformulation.

$($b$).$ Compute the U$-$O link flow and travel demand pattern.

$($c$).$ Verify that the pattern you computed in $($b$)$ is a U$-$O pattern for the elastic demand problem.