2 The network models a cooling system in a factory. Coolant starts at \(A , B\) and \(C\) and flows through the system. The arcs model components of the cooling system and the weights show the maximum amount of coolant that can flow through each component of the system (measured in litres per second). The arrows show the direction of flow.
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1. Add a supersource, \(S\), and a supersink, \(T\), to the copy of the network in your answer book. Connect \(S\) and \(T\) to the network using appropriately weighted arcs.
2. (a) Find the capacity of the cut that separates \(A , B , C\) and \(E\) from \(D , F , G\) and \(H\).
   (b) Find the capacity of the cut that separates \(A , B , C , D , E\) and \(F\) from \(G\) and \(H\).
   (c) What can you deduce from this value about the maximum flow through the system?
3. Find the maximum possible flow through the system and prove that this is the maximum.
4. Describe what effect increasing the capacity of \(C E\) would have on the maximum flow.