6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5274a614-7862-49f0-ad1d-b59b73aa51ad-07_983_1513_210_283}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a capacitated, directed network. The network represents a system of pipes through which fluid flows from a source, S , to a sink, T .
The numbers ( \(l , u\) ) on each arc represent, in litres per second, the lower capacity, \(l\), and the upper capacity, \(u\), of the corresponding pipe.
Two cuts \(C _ { 1 }\) and \(C _ { 2 }\) are shown.
- Find the capacity of
- \(\operatorname { cut } C _ { 1 }\)
- \(\operatorname { cut } C _ { 2 }\)
- Explain why the arcs AE and CE cannot be at their upper capacities simultaneously.
- Explain why a flow of 31 litres per second through the system is not possible.
- Hence determine a minimum feasible flow and a maximum feasible flow through the system. You must draw these feasible flows on the diagrams in the answer book and give reasons to justify your answer. You should not apply the labelling procedure to find these flows.