6 [Figures 3, 4 and 5, printed on the insert, are provided for use in this question.]\\
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]{1bf0d8b7-9f91-437a-bc18-3bfe5ca12223-07_849_1363_518_326}
\begin{enumerate}[label=(\alph*)]
\item Find the value of the cut $C$.
\item Figure 3, on the insert, shows a partially completed diagram for a feasible flow of 40 litres per second from $S$ to $T$. Indicate, on Figure 3, the flows along the edges $A E , E F$ and $F G$.
\item \begin{enumerate}[label=(\roman*)]
\item Taking your answer from part (b) as an initial flow, indicate potential increases and decreases of the flow along each edge on Figure 4.
\item Use flow augmentation on Figure 4 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 Illustrate the maximum flow on Figure 5.
\item Find a cut with value equal to that of the maximum flow.
\end{enumerate}

\hfill \mbox{\textit{AQA D2 2009 Q6 [16]}}