Determine a maximum s$-$t flow and an s$-$t cut of minimum capacity in the following directed graphs using the maximum flow algorithm, where the numbers indicate the capacities:

$3\mathrm{.}11.$

$($iv$)$ For each augmenting path you add, include a sketch $($with the value of the flow through that path$)$; the graph with the found maximum flow drawn in $($and the value of that flow$)$; from this last graph, also include the complete residual graph, so including arrows in the reverse direction if there is flow through the arrow; the points circled from the set.