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

The maximum flow is not unique. For any $x\in [1,2]$, setand split the flow from $b$ byFlow conservation then requiresAll capacities are respected precisely throughout the displayed interval, and every member of this one-parameter family has value $8$. For example, $x=1$ and $x=2$ give distinct maximum flows.