A$.(15$ points$)$ The phrase "find the general traffic pattern" means to state the complete set of all possible combina$-$

tions of traffic flows in the network. Assume that traffic must travel in the directions shown $($so no traffic flows

are negative$).$ You can use python to answer this question if you like. If you use python, show all the code you

ran, including input and output.

$($a$)$ Find the general traffic pattern in the freeway network short in the figure. $($Flow rates are in cars $/$ minute.$)$

$($b$)$ Find the general traffic pattern when the road whose flow is $x_4$ is closed.

$($c$)$ Now assume the flow out of the system from node $D$ is no longer $40$ but instead is $35.$ What is the solution

to the new system? Explain why you get this answer.