Consider the following flow network with a flow $f$ shown. An edge labelled $"b"$ means that it

has capacity $b$ and flow $0.$ An edge labelled $"\frac{a}{b}"$ means that the flow on that edge is a and

the capacity is $b.$

$($a$)(10$ points$)$ Draw the residual graph $G_f.$

$($s$)$

$($s$)$

$($b$)$

$($c$)$

$($t$)$

$($b$)(3$ points$)$ What augmenting path in this graph would result in the greatest increase in

flow value? $($List the names of the vertices on this path in order.$)$

$($c$)(7$ points$)$ On the diagram below, indicate the new flow values resulting from augmenting

along the path you found in part $($b$).$