Past exam of the mathematics course of the University of Cambridge / 2019 / ib / Paper 4 / 20H / b / ii / Solution

After these augmentations, the vertices reachable from $S$ in the residual network areThe edges leaving this set are $S\to b$, $a\to d$, and $c\to e$, with capacities $3$, $1$, and $4$. HenceThe flow in part (i) has the same value, so the max-flow min-cut theorem proves that it is maximum and that this cut is minimum.