6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a2bc4f5d-f7db-4ce7-860b-f53a743c7e2c-7_821_1433_205_317}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\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.
- Calculate the value of the cut \(C _ { 1 }\) and cut \(C _ { 2 }\)
- Explain why the flow through the network must be at least 12 and at most 16
- Explain why arcs DG, AG, EG and FG must all be at their lower capacities.
- 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.
- State the value of the maximum flow through the network.
- 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.
- Explain how it is possible to maintain the maximum flow found in (d).