Let a network be given by nodes V = {S, A, B, C, D, T} and arcs, capacities c and a flow f according to the table: SA SC AB BT AC DC BD DT AT CT f ? 3 4 1 0 ? ? 1 3 ? C 9 3 5 1 1 2 3 4 3 5 (a) Complete f and c 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?