$8($lo pis$)$ Maximum Flows. Answer in $30$ minutes please

consider the following flow network and feasible flow f from the source vertex $s.$ th$.$ th

$($a$)[3$ pts$]$ What is the value of the flow $f?$ Circle the correct answer.

$3$

$5$

$7$

$11$

$13$

$17$

$($b$)[3$ pts$]$ Starting from the flow given above, perform one iteration of the Ford$-$Fulkerson algorithm. List the sequence of vertices on the augmenting path, in order from $S$ to $T.$

$($c$)[2$ pts$]$ What is the value of the maximum flow? Circle the only one correct answer.

$3$

$5$

$7$

$11$

$13$

$17$

$($d$)[2$ pts$]$ Circle all vertices on the sink $($T$)$ side of the minimum cut.

S

A

B

C

D

E