2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a12f9520-85c0-43f6-a104-2502011d5657-3_780_1155_246_461}
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\caption{Figure 1}
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Figure 1 shows a capacitated, directed network of pipes. The number on each arc represents the capacity of the corresponding pipe. The numbers in circles represent an initial flow.
- List the saturated arcs.
- State the value of the initial flow.
- State the capacities of the cuts \(C _ { 1 }\) and \(C _ { 2 }\)
- By inspection, find a flow-augmenting route to increase the flow by three units. You must state your route.
- Prove that the new flow is maximal.