6.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{a2bc4f5d-f7db-4ce7-860b-f53a743c7e2c-7_821_1433_205_317}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}

Figure 1 shows a capacitated, directed network. The number on each arc $( x , y )$ represents the lower $( x )$ capacity and upper $( y )$ capacity of that arc.
\begin{enumerate}[label=(\alph*)]
\item Calculate the value of the cut $C _ { 1 }$ and cut $C _ { 2 }$
\item Explain why the flow through the network must be at least 12 and at most 16
\item Explain why arcs DG, AG, EG and FG must all be at their lower capacities.
\item Determine a maximum flow pattern for this network and draw it on Diagram 1 in the answer book. You do not need to use the labelling procedure.
\item \begin{enumerate}[label=(\roman*)]
\item State the value of the maximum flow through the network.
\item Explain why the value of the maximum flow is equal to the value of the minimum flow through the network.

Node E becomes blocked and no flow can pass through it. To maintain the maximum flow through the network the upper capacity of exactly one arc is increased.
\end{enumerate}\item Explain how it is possible to maintain the maximum flow found in (d).
\end{enumerate}

\hfill \mbox{\textit{Edexcel FD2  Q6 [12]}}