Civil Engineering, show the work for everything even lambda

Question $2(25$ marks$).$

Consider the $3$ zone system shown below, with a $6$ link road network.

$5000$ vehicles are travelling from Zone $1$ to Zone $3.$

$5000$ vehicles are travelling from Zone $2$ to Zone $3.$

All links have a BPR function of the following form:

$S(Vl)=(t_0)**[1+(\frac{V}{C}{)}^b]$

Note that the following integration may be helpful in solving this question.

${\displaystyle \underset{0}{\overset{V^{\text{'}\text{'}}}{}}}(t_0)**[1+(\frac{V}{C}{)}^b]dv=(t_0)(V^{\text{'}\text{'}}+\frac{C**(\frac{V^{\text{'}\text{'}}}{C}{)}^{b+1}}{b+1})$

Link attributes are shown in the attached table.

$\backslash$table$[[$Link$,\backslash$table$[[t_0$