5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a91f96a3-a9b4-4bf5-bfdf-93c34912e54a-6_1012_1696_233_182}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 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) - State the capacities of cuts \(\mathrm { C } _ { 1 }\) and \(\mathrm { C } _ { 2 }\).
(2) - By entering values along DH, FH, FI and IT, complete the labelling procedure on Diagram 1 in the answer book.
(2) - Using Diagram 1, increase the flow by a further 4 units. You must list each flow-augmenting route you use, together with its flow.
(3) - Prove that the flow is now maximal.
(2)