Problem $4$: Traffic Assignment $(25$ points$)$

An origin is connected to a destination with two links. The capacity of link $1$ is $3,000ve\frac{h}{h},$ and the free$-$flow travel time $($FFTT$)$ is $15$ minutes. The capacity of link $2$ is $2,000ve\frac{h}{h},$ with a FFTT of $18$ minutes. The total demand from origin to destination is $4,000ve\frac{h}{h}.$ The actual travel time has the following form:

$T{T}_i=FFT{T}_i*(1+\frac{V_i}{C_i})$

$i=$ link number $(1,2)$

${}_i-$ actual travel time $on$ link $i(min)$

$FF{T}_i-$ free$-$flow travel time $on$ link $i(min)$

$V_i-$ volume $on$ link $i($ veh $\frac{?}{?}h)$

$C_i-$ capacity $of$ link $i(ve\frac{h}{h})$

$FFT{T}_i-$ free$-$flow travel time on link $i($min$)$

$V_i-$ volume on link $i($veh$/$h$)$

$C_i-$ capacity of link $i($veh$/$h$)$

Using en analytical approach, determine the flows on links $1$ and $2$ so that the User Equilibrium is achieved $($i$.$e$.$ actual travel times on both links are the same$).$