5 [Answer this question on the insert provided.]\\
Fig. 1 shows a directed flow network. The weight on each arc shows the capacity in litres per second.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{09279013-7088-4db2-99dd-098b32fbcad7-05_620_1082_424_502}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}

(i) Find the capacity of the cut $\mathscr { C }$ shown.\\
(ii) Deduce that there is no possible flow from $S$ to $T$ in which both arcs leading into $T$ are saturated. Explain your reasoning clearly.

Fig. 2 shows a possible flow of 160 litres per second through the network.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{09279013-7088-4db2-99dd-098b32fbcad7-05_499_1084_1471_500}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}

(iii) On the diagram in the insert, show the excess capacities and potential backflows for this flow.\\
(iv) Use the labelling procedure to augment the flow as much as possible. Show your working clearly, but do not obscure your answer to part (iii).\\
(v) Show the final flow that results from part (iv). Explain clearly how you know that this flow is maximal.

\hfill \mbox{\textit{OCR D2  Q5 [14]}}