Consider the network shown in Figure $6\mathrm{.}22($a$)$ together with the feasible flow x $(8$iven

in the figure.

$($a$)$ Specify four s$-$t cuts in the network, each containing four forward arcs. List the

capacity, residual capacity, and the flow across each cut.

$($b$)$ Draw the residual network for the network given in Figure $6\mathrm{.}22($a$)$ and list four

augmenting paths from node s to node t$.$