Let a network be given by nodes V = {S, A, B,C, D,T} and ares, capacities e and a flow f according to the table: SA SC AB вТ АС DC BD DT AT CT 3 4 1 0 3 5 1 1 ? ? 1 3 ? 9 2 3 4 3 5 (a) Complete f and e such that f is an admissible flow from S to T. Justify your answer. What is the value of the flow? (b) Determine a maximal flow from S to T and a minimal cut with its capacity by the augmenting path method starting by the flow f from (a). (c) What is the relation between each admissible flow and each cut? (d) What is the relation between the maximum flow and the minimum cut?

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