8.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 4}
  \includegraphics[alt={},max width=\textwidth]{c4c64221-0373-4be9-abe3-5ff281922cdb-07_521_1404_285_343}
\end{center}
\end{figure}

The network in Fig. 4 models a drainage system. The number on each arc indicates the capacity of that arc, in litres per second.
\begin{enumerate}[label=(\alph*)]
\item Write down the source vertices.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 5}
  \includegraphics[alt={},max width=\textwidth]{c4c64221-0373-4be9-abe3-5ff281922cdb-07_521_1402_1170_343}
\end{center}
\end{figure}

Figure 5 shows a feasible flow through the same network.
\item State the value of the feasible flow shown in Fig. 5.

Taking the flow in Fig. 5 as your initial flow pattern,
\item use the labelling procedure on Diagram 1 to find a maximum flow through this network. You should list each flow-augmenting route you use, together with its flow.
\item Show the maximal flow on Diagram 2 and state its value.
\item Prove that your flow is maximal.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D2 2002 Q8 [14]}}