Consider the following distribution network that supports the flow of products from Node-1 to Node-6. Numbers next to each arc represents its capacity and the flow respectively. In order to determine the capacity of this network, so far you have figured out a way to ship 14 units from Node-1 to Node-6 as shown in the figure below.

1. For the flows given in Figure, is Node 1 Node 2 Node 4 Node 3 Node 5 Node 6 a Flow Augmenting path? If yes, how much additional flow you can send along this path. Discuss.

2. Starting with flows given in Figure (with a total flow of 14 so far), use the Flow Augmenting path method to find the capacity of this network. At each iteration, use a FAP that allows maximum additional flow. At each iteration, do not simply find the path by inspection but show the process (Labeling Method you use in general to find such a FAP). In the end, identify the bottleneck arcs.

7 3 2 4 15 3 11 11 14 8 8 14 200 100 1 6 15 11 15 3 3 5 103 Capacity Flow STARTING FLOWS: 7 2 4 73 11 2 15 11 11 8 15 3 14 88 20 14 1 10 6 1 200 100 6 15 15 15 11 3 5 15 3 10 3 5 103 Capacity Flow 7 2 4 2 4 15 11 11 15 8 8 1 20 10 6 20 101 1 6 15 15 15 15 3 5 3 5 10 100 7 3 2 4 15 3 11 11 14 8 8 14 200 100 1 6 15 11 15 3 3 5 103 Capacity Flow STARTING FLOWS: 7 2 4 73 11 2 15 11 11 8 15 3 14 88 20 14 1 10 6 1 200 100 6 15 15 15 11 3 5 15 3 10 3 5 103 Capacity Flow 7 2 4 2 4 15 11 11 15 8 8 1 20 10 6 20 101 1 6 15 15 15 15 3 5 3 5 10 100