Section I. The following digraph represents a network flow problem with values at nodes showing net demand.

a$.$ Verify that total supply exceeds total demand.

b$.$ Add a sink to create an equivalent network with total supply equal to total demand.

Section II$.$ Consider the following digraph.

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.