(3) The Shortest Augmenting Path Algorithm. Consider the following maximum flow problem. (Arc capacities are shown.) (a) Apply the Ford-Fulkerson algorithm to find a maximum s - t flow. Use the shortest augmenting path method to chose the augmenting path in each iteration. [In the case of a tie, break ties lexicographically; that is, select the augmenting path alphabetically.] (b) Prove that your solutions give maximum s-t flows by giving a certificate that shows it is impossible to find a larger flow