Question: 3. You are given a network with 6 nodes (labeled 1, 2, 3, 4, 5, 6) and 9 arcs. The arcs, their capacities and the

3. You are given a network with 6 nodes (labeled

3. You are given a network with 6 nodes (labeled 1, 2, 3, 4, 5, 6) and 9 arcs. The arcs, their capacities and the current flow through the arcs are given below. Arc 1 + 2 1 +3 1 +4 1 +5 2 + 4 3 +5 3 +6 4 +6 5 +6 Capacity Current flow 20 20 30 30 30 0 40 30 20 20 20 0 40 30 20 20 30 30 (a) (points: 5) Draw the network along with the capacities and the flow. Verify whether the current flow is a maximum flow. 2 (b) (points: 5) A new arc 2 + 3 is laid in the network with capacity 20. Is the current flow a maximum flow in the new network? Justify your answer. If it is not a maximum flow, find a maximum flow in the new network

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