2. (DPV 7.17) Consider the following network (the numbers associated with the edges are the edge capacities) 6 a. Find the maximum flow f and a minimum cut b. Draw the final residual graph Gf (along with its edge capacities). In this residual network, mark the vertices reachable from S and the vertices from which T is reachable. c. An edge of a network is called a bottleneck edge if increasing its capacity results in an increase in d. Give a very simple example (containing at most four vertices) of a network which has no bottleneck e. Give an efficient algorithm to identify all bottleneck edges in a network. (Hint: Execute a known the maximum flow. List all bottleneck edges in the above network. edges. network flow algorithm (e.g., Ford-Fulkerson), and then examine the residual graph.)