B$.(7$ pts$)$ Intersections in Massachusetts are often constructed as one$-$way "rotaries," such as the one shown in the

figure. Assume that traffic must travel in the directions shown. Find the general solution of the network flow.

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 solution of the network flow.

$($b$)$ Find the smallest possible value for $x_6.$