Consider the directed network $(D,c)$ given by the

following drawing, where each arc einA$(D)$ is labelled by its capacity $c(e)$ and two

vertices $s$ and $t$ have been identified.

$($a$)$ Use the Ford$-$Fulkerson algorithm to find a maximum $s-t-$flow of $(D,c).$ Draw

the residual network after each iteration of the algorithm and give the size of the

maximum flow.

$($b$)$ Give a minimum $s-t-$cut of $(D,c).$ Justify your answer and give the capacity of

the cut.