2. (50 points) [Max Flow] Consider the following network G. (a) (5 points) Define a source vertex and a sink vertex. Identify the source and sink in G. (b) (30 points) Trace the Edmonds-Karp maximum flow algorithm (where each new augmenting path is founding using a BFS from the source vertex) on G. Whenever faced with a decision of which vertex to pick from a set of vertices during the BFS, pick the vertex whose label occurs earliest in the alphabet. Show the augmenting path chosen in each step, the flow of that path, and the resulting final flow for each edge. (c) (5 points) What is the value of the maximum flow f ? (d) (10 points) Identify in G a cut with minimum capacity