Part III: Traffic Assignment $($topt$)$

Given the following network with $5$ rodes, the number on a link refers to the free flow travel time in minute. For example, the free flow travel time from node $1$ to node $2$ is $5$ minutes; and that from node $2$ to node $4$ is $3$ minutes.

All links, expect diagonal links, have capacity of $2400ve\frac{h}{h}r.$ Two diagonal links: $25$ and $34$ have capacity of $3200ve\frac{h}{h}r,$ respectively.

To the link performance function, apply the BPR function $t=t_0[1+(\frac{x}{c}{)}^{}],$ where $t_0$ refers to the free flow travel time; $c$ refers to the capacity; and two parameters $=0\mathrm{.}15,=4.$ Only consider the travel demand from node $1$ to node $5,$ which is $5000ve\frac{h}{h}r.$

Answer the following questions. You are recommended to use Excel to solve this UE and SO problem.

List all acyclic paths from node $1$ to node $5.(10pt)$