1.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ae354c58-6de8-4f94-b404-2f0feecb5bf3-02_953_1687_251_191}
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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 that pipe. The numbers in circles represent a feasible flow from S to T .
- State the value of the feasible flow.
(1) - Find the capacity of cut \(\mathrm { C } _ { 1 }\) and the capacity of cut \(\mathrm { C } _ { 2 }\)
(2) - By inspection, find a flow-augmenting route to increase the flow by two units. You must state your route.
(1) - Prove that, once the flow-augmenting route found in (c) has been applied, the flow is now maximal.
(3)