Given a flow network as below with S and T as source and sink (destination). The pair of integers on each edge corresponds to the flow value and the capacity of that edge. For instance, the edge (S,A)...

Given a flow network as below with S and T as source and sink (destination). The pair of integers on each edge corresponds to the flow value and the capacity of that edge. For instance, the edge (S,A) has capacity 16 and currently is assigned a flow of 5 (units). Assume that we are using the Ford-Fullkerson's method to find a maximum flow for this problem. Fill in the blanks below with your answers.

a) What is the
augmenting path
in the corresponding
residual network?

Note: give you answer by listing the vertices along the path, starting with S and ending with T, e.g.,SADT(note that this is for demonstration purpose only and may not be a valid answer), withno spaces or punctuation marks, i.e., no commas "," or full stops ".". If there are more than one augmenting path, then you can choose one arbitrarily.

b) What is the
maximum increase
of the flow value that can be applied along the augmenting path identified in Part a)?

c) What is the
value of a maximum flow?

Note: your answers for Part b) and Part c) are a single integer with no spaces before or after.