This question has four parts. You have to answer all for full credit.

Consider the following st$-$flow network and the given feasible flow $f.$

$($a$)$ What is the value of the current flow f$?$

$($b$)$ What are the two constraints of a flow? Verify that $f$ is a feasible flow in this

network.

$($c$)$ Perform one iteration of the Ford$-$Fulkerson algorithm, starting from the

flow $f.$ Give the

sequence of vertices on an augmented path. Draw the residual graph, and

show the path you chose.

$($d$)$ What is the value of the maximum flow? $($Justify your answer using the final

residual graph$)$