Network Flow

Here is a network$-$flow graph $G.$ The source node is node $a,$ and the sink node is node $f.$ The label on each edge shows flow$/$capacity$.$

Starting with the existing flow, do two steps of Ford$-$Fulkerson to compute a max flow on this network. For each step of F$-$F:

draw the residual graph $[5$ points$]$

identify an augmenting path in the residual graph and say what the bottleneck value is $[2$ points$]$

augment the flow and draw the updated flow network $[3$ points$]$

Finally, clearly show a min cut in the final graph. $[2$ points$]$