$($a$)$

$($b$)$

$($a$)$ A flow network G $=($V$,$ E$)$ for the Lucky Puck Company's trucking problem.

The Vancouver factory is the source $\backslash ($ s $\backslash ),$ and the Winnipeg warehouse is the sink $\backslash ($ t $\backslash ).$ The company ships pucks through intermediate cities, but only $\backslash ($ c$($u$,$ v$)\backslash )$ crates per day can go from city u to city v $.$ Each edge is labeled with its capacity.

$($b$)$ A flow $\backslash ($ f $\backslash )$ in $\backslash ($ G $\backslash )$ with value $\backslash (|$f$|=19\backslash ).$ Each edge $\backslash (($u$,$ v$)\backslash )$ is labeled by $\backslash ($ f$($u$,$ v$)/$ c$($u$,$ v$)\backslash ).$

Use the Ford$-$Fulkerson algorithm to find the maximum flow from $\backslash ($ s $\backslash )($source$)$ to $\backslash ($ t $\backslash )($sink$).$ Also, identify the minimum cut, i$.$e$.,$ set of edges $($with smallest capacity$)$ which, if removed, would entirely block traffic$/$flow from $\backslash ($ s $\backslash )$ to $\backslash ($ t $\backslash ).$