a$.$ Starting from an all zero flow, apply Bellman Ford Algorithm to compute a max flow from node $s$ to node $t.$ Show the residual digraph at each iteration, and choose your augmenting paths by inspection.

b$.$ Process the final residual digraph of $($a$)$ to identify a min cut, and verify that max flow $=$ min cut in this instance.

c$.$ Repeat parts $($a$)$ and $($b$),$ this time augmenting along shortest cardinality paths in the residual digraphs.

d$.$ Comment on how results of the two computations differ if at all, and why.