6. (a) Define the term 'cut' as it applies to a directed network.
(2)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7396d930-0143-4876-b019-a4d73e09b172-7_659_1367_376_349}
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\caption{Figure 6}
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Figure 6 shows a capacitated, directed network. The number on each arc represents the capacity of that arc. The numbers in circles represent an initial flow.
(b) Complete the labelling procedure on Diagram 2 in your answer book by entering values along CE, EG, HT and GT.
(c) Find the maximum flow through the network. You must list each flow-augmenting route you use together with its flow.
(d) Show a maximal flow pattern on Diagram 3 in your answer book.
(e) State the value of the maximum flow through the network.
(f) Prove that your flow is maximal.