6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5798c81-290a-4e4b-aa46-497b62ca899b-07_1155_1541_223_264}
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\caption{Figure 1}
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Figure 1 shows a capacitated, directed network. The number on each arc represents the capacity of the corresponding arc. The numbers in circles represent an initial flow from S to T .
- State the value of the initial flow.
- State the capacity of cut \(C _ { 1 }\)
- Complete the initialisation of the labelling procedure on Diagram 1 in the answer book by entering values along \(\mathrm { AC } , \mathrm { SB } , \mathrm { BE } , \mathrm { DE }\) and FG .
(2) - Hence use the labelling procedure to find a maximum flow through the network. You must list each flow-augmenting route you use, together with its flow.
- Draw a maximal flow pattern on Diagram 2 in the answer book.
- Prove that your flow is maximal.