3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f3feef8a-32ba-4234-a5fa-cdd26ef6967d-4_778_1420_262_360}
\captionsetup{labelformat=empty}
\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.
- State the capacity of cut \(\mathrm { C } _ { 1 }\).
The labelling procedure has been used and the result drawn on Diagram 1 in the answer book.
- Use Diagram 1 to find the maximum flow through the network. You must list each flow-augmenting route you use, together with its flow.
(4) - Draw a maximum flow pattern on Diagram 2 in your answer book.
(2) - Prove that the flow shown in (d) is maximal.
(2)