3 Answer this question on the insert provided. \begin{figure}[h] \end{figure} Fig. 1 represents a system of pipes through which fluid can flow from a source, \(S\), to a sink, \(T\). It also shows a cut \(\alpha\). The weights on the arcs show the lower and upper capacities of the pipes in litres per second.

1. Calculate the capacity of the cut \(\alpha\).
2. By considering vertex \(B\), explain why arc \(S B\) must be at its lower capacity. Then by considering vertex \(E\), explain why arc \(C E\) must be at its upper capacity, and hence explain why arc \(H T\) must be at its lower capacity.
3. On the diagram in the insert, show a flow through the network of 15 litres per second. Write down one flow augmenting route that allows another 1 litre per second to flow through the network. Show that the maximum flow is 16 litres per second by finding a cut of 16 litres per second. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{c5bfbe78-64c4-4254-ad83-0c90f4a54b18-4_602_1086_1809_568} \captionsetup{labelformat=empty} \caption{Fig. 2}
   \end{figure} Fig. 2 represents the same system, but with pipe \(E B\) installed the wrong way round.
4. Explain why there can be no feasible flow through this network.