4 [Figures 3, 4 and 5, 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. Figure 3, on the insert, shows a partially completed diagram for a feasible flow of 10 litres per second from \(S\) to \(T\). Indicate, on Figure 3, the flows along the edges \(M N , P Q , N P\) and \(N T\).
2. 1. Taking your answer from part (a) as an initial flow, use flow augmentation on Figure 4 to find the maximum flow from \(S\) to \(T\).
   2. State the value of the maximum flow and illustrate this flow on Figure 5.
3. Find a cut with capacity equal to that of the maximum flow.