- A sheet is provided for use in answering this question.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b8eb80d5-5af5-4a8b-8335-6fae95f3aa73-3_881_1310_319_315}
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\caption{Fig. 2}
\end{figure}
Figure 2 shows a capacitated, directed network.
The numbers in bold denote the capacities of each arc.
The numbers in circles show a feasible flow of 48 through the network.
- Find the values of \(x\) and \(y\).
- Use the labelling procedure to find the maximum flow through this network, listing each flow-augmenting route you use together with its flow.
- Show your maximum flow pattern and state its value.
- Find a minimum cut, listing the arcs through which it passes.
- Explain why this proves that the flow found in part (b) is a maximum.