Consider the following maximum flow problem. (Edge capacities are shown.) Apply the Ford-Fulkerson algorithm to find a maximum s-t flow. Use the shortest augmenting path method to choose the augmenting path in each iteration. Repeat (a), but now use the maximum capacity augmenting path method to choose the augmenting path in each iteration. (c) Prove that your solutions give maximum s-t flows by giving a certificate that shows it is impossible to find a larger flow