7 The network shows a system of pipes, where \(S\) is the source and \(T\) is the sink.
The capacity, in litres per second, of each pipe is shown on each arc.
The cut shown in the diagram can be represented as \(\{ S , P , R \} , \{ Q , T \}\).
\includegraphics[max width=\textwidth, alt={}, center]{ba9e9840-ce27-4ca7-ab05-50461d135445-10_629_1168_616_557} 7

1. Complete the table below to give the value of each of the 8 possible cuts.

   Cut		Value
   \{ S \}	\(\{ P , Q , R , T \}\)	31
   \(\{ S , P \}\)	\(\{ Q , R , T \}\)	32
   \(\{ S , Q \}\)	\(\{ P , R , T \}\)
   \(\{ S , R \}\)	\(\{ P , Q , T \}\)
   \(\{ S , P , Q \}\)	\(\{ R , T \}\)	30
   \(\{ S , P , R \}\)	\(\{ Q , T \}\)	37
   \(\{ S , Q , R \}\)	\(\{ P , T \}\)	35
   \(\{ S , P , Q , R \}\)	\(\{ T \}\)	30

   7
2. State the value of the maximum flow through the network. Give a reason for your answer.
   [0pt] [1 mark] 7
3. Indicate on Figure 1 a possible flow along each arc, corresponding to the maximum flow through the network.
   [0pt] [2 marks] \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{ba9e9840-ce27-4ca7-ab05-50461d135445-11_618_1150_1260_557}
   \end{figure}