6 The network shows a system of pipes with the lower and upper capacities for each pipe in litres per second.\\
\includegraphics[max width=\textwidth, alt={}, center]{b23828c8-01ee-4b5a-b6d2-41b7e27190d6-14_807_1472_429_276}
\begin{enumerate}[label=(\alph*)]
\item Find the value of the cut $Q$.
\item Figure 2 shows most of the values of a feasible flow of 34 litres per second from $S$ to $T$.
\begin{enumerate}[label=(\roman*)]
\item Insert the missing values of the flows along $D E$ and $F G$ on Figure 2.
\item Using this feasible flow as the initial flow, indicate potential increases and decreases of the flow along each edge on Figure 3.
\item Use flow augmentation on Figure 3 to find the maximum flow from $S$ to $T$. You should indicate any flow-augmenting paths in the table and modify the potential increases and decreases of the flow on the network.
\end{enumerate}\item \begin{enumerate}[label=(\roman*)]
\item State the value of the maximum flow.
\item Illustrate your maximum flow on Figure 4.
\end{enumerate}\item Find a cut with capacity equal to that of the maximum flow.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 2}
  \includegraphics[alt={},max width=\textwidth]{b23828c8-01ee-4b5a-b6d2-41b7e27190d6-15_1646_1463_280_381}
\end{center}
\end{figure}

Figure 3

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 4}
  \includegraphics[alt={},max width=\textwidth]{b23828c8-01ee-4b5a-b6d2-41b7e27190d6-15_668_1230_1998_404}
\end{center}
\end{figure}
\end{enumerate}

\hfill \mbox{\textit{AQA D2 2012 Q6 [14]}}