6 The network shows a system of pipes with lower and upper capacities for each pipe in litres per second.\\
\includegraphics[max width=\textwidth, alt={}, center]{34de3f03-a275-44fb-88b2-b88038bcec97-22_817_744_397_648}
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find the value of the cut $X$.
\item Hence state what can be deduced about the maximum flow from $A$ to $H$.
\end{enumerate}\item Figure 3 shows a partially completed diagram for a feasible flow of 28 litres per second from $A$ to $H$.

Indicate, on Figure 3, the flows along the edges $B D , B E$ and $C D$.
\item \begin{enumerate}[label=(\roman*)]
\item Using your feasible flow 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 $A$ to $H$. You should indicate any flow augmenting paths in the table and modify the potential increases and decreases of the flow on the network.
\item State the maximum flow and indicate a maximum flow on Figure 5.

\section*{Answer space for question 6}
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 3}
  \includegraphics[alt={},max width=\textwidth]{34de3f03-a275-44fb-88b2-b88038bcec97-23_682_689_312_397}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 4}
  \includegraphics[alt={},max width=\textwidth]{34de3f03-a275-44fb-88b2-b88038bcec97-23_935_1477_1037_365}
\end{center}
\end{figure}

Figure 5

\begin{center}
\includegraphics[max width=\textwidth, alt={}]{34de3f03-a275-44fb-88b2-b88038bcec97-24_2032_1707_219_153}
\end{center}
\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{AQA D2 2016 Q6 [14]}}