6 [Figures 4, 5 and 6, printed on the insert, are provided for use in this question.]
The network shows a system of pipes with the lower and upper capacities for each pipe in litres per second.
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1. 1. Find the value of the cut \(C\).
   2. State what can be deduced about the maximum flow from \(S\) to \(T\).
2. Figure 4, printed on the insert, shows a partially completed diagram for a feasible flow of 20 litres per second from \(S\) to \(T\). Indicate, on Figure 4, the flows along the edges \(M P , P N , Q R\) and \(N R\).
3. 1. Taking your answer from part (b) as an initial flow, indicate potential increases and decreases of the flow along each edge on Figure 5.
   2. Use flow augmentation on Figure 5 to find the maximum flow from \(S\) to \(T\). You should indicate any flow augmenting paths in the table and modify the potential increases and decreases of the flow on the network.
   3. Illustrate the maximum flow on Figure 6.