2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{261e22b8-0063-419c-a388-6831a427fb65-03_860_1705_276_182}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a capacitated, directed network. The number on each arc represents the capacity of that arc. The numbers in circles represent an initial flow.
- State the value of the initial flow.
(1) - Obtain the capacity of the cut that passes through the arcs \(\mathrm { AG } , \mathrm { CG } , \mathrm { GF } , \mathrm { FT } , \mathrm { FH }\) and EH .
(1) - Complete the initialisation of the labelling procedure on Diagram 1 in the answer book by entering values along \(\mathrm { SD } , \mathrm { BD } , \mathrm { BE }\) and GF .
(2) - 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.
(3) - Use the answer to part (d) to add a maximum flow pattern to Diagram 2 in the answer book.
(1) - Prove that your answer to part (e) is optimal.
(3)