5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{be646775-535e-4105-86b4-ffc7eda4fa51-5_819_1421_251_322}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Figure 5 shows a capacitated, directed network of pipes. The number on each arc represents the capacity of that pipe. The numbers in circles represent a feasible flow.
- State the values of \(x\) and \(y\).
- List the saturated arcs.
- State the value of the feasible flow.
- State the capacities of the cuts \(\mathrm { C } _ { 1 } , \mathrm { C } _ { 2 }\), and \(\mathrm { C } _ { 3 }\).
- By inspection, find a flow-augmenting route to increase the flow by one unit. You must state your route.
- Prove that the new flow is maximal.