1 The network represents a system of pipes along which fluid can flow from \(S\) to \(T\). The values on the arcs are lower and upper capacities in litres per second.
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1. Calculate the capacity of the cut with \(\mathrm { X } = \{ S , A , B , C \} , \mathrm { Y } = \{ D , E , F , G , H , I , T \}\).
2. Show that the capacity of the cut \(\alpha\), shown on the diagram, is 12 litres per second and calculate the minimum flow across the cut \(\alpha\), from \(S\) to \(T\), (without regard to the remainder of the diagram).
3. Explain why the arc SC must have at least 5 litres per second flowing through it. By considering the flow through \(A\), explain why \(A D\) cannot be full to capacity.
4. Show that it is possible for 11 litres per second to flow through the system.
5. From your previous answers, what can be deduced about the maximum flow through the system?