STARTING FLOWS: Consider the following distribution network that supports 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 figure below.STARTING FLOWS: STARTING FLOWS:

$($a$)$ For the flows given in Figure on previous page, 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.

STARTING FLOWS:$($b$)$ Starting with flows given in Figure on previous page $($with total flow of $14$ so far$),$ use Flow Augmenting path method to find the capacity of this network. At each iteration, determine the FAP that allows maximum additional flow. At each iteration, do not simply find the path by inspection but show the process step$-$by$-$step $($Labeling Method you use in general to find such a FAP$).$ You can use copies of the figures at the back of the exam to show details of your work. At the end, identify the bottleneck arcs.