3. This question should be answered on the sheet provided.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{acc09687-11a3-4392-af17-3d4d331d5ab4-04_883_1317_317_315}
\captionsetup{labelformat=empty}
\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.
(2 marks)