Consider the following flow network.

Let $S=\{s,u,x\}$ and $T=\{v,w,y,z,t\}$

$($a$)(5$ points$)$ What is $f(S,T)?$

$($b$)(5$ points$)$ What is $c(S,T)?$

$($c$)(20$ points$)$ Find a minimum cut for $G($Hint: Add augmenting

paths until no augmenting path can be found. Which edges are

reachable from $s$ in the $G_f?)$