9.\\
\includegraphics[max width=\textwidth, alt={}, center]{be329a47-a709-4719-abe6-41d388a6c631-6_540_1291_203_411}

This diagram shows a capacitated directed network. The number on each arc is its capacity.
\begin{enumerate}[label=(\alph*)]
\item State the maximum flow along
\begin{enumerate}[label=(\roman*)]
\item SADT,
\item SCET,
\item $S B F T$.
\end{enumerate}\item Show these maximum flows on Diagram 1 below.

\section*{Diagram 1}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{be329a47-a709-4719-abe6-41d388a6c631-6_561_1187_1283_721}
\end{center}

Take your answer to part (b) as the initial flow pattern.
\item \begin{enumerate}[label=(\roman*)]
\item Use the labelling procedure to find a maximum flow from $S$ to $T$. Your working should be shown on Diagram 2 below. List each flow-augmenting route you use, together with its flow.

\section*{Diagram 2}
\includegraphics[max width=\textwidth, alt={}, center]{be329a47-a709-4719-abe6-41d388a6c631-7_718_1525_205_269}
\item Draw your final flow pattern on Diagram 3 below.\\
\includegraphics[max width=\textwidth, alt={}, center]{be329a47-a709-4719-abe6-41d388a6c631-7_611_1196_1082_717}
\item Prove that your flow is maximal.
\end{enumerate}\item Give an example of a practical situation that could have been modelled by the original network.
\end{enumerate}

\hfill \mbox{\textit{Edexcel D2 2005 Q9 [14]}}