$6\mathrm{.}12.$ Consider the network shown in Figure $6\mathrm{.}22($a$)$ together with the feasible flow $x$ given

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 $t.$

$($a$)$

$($b$)$