(1) The Marimum Capacity Augmenting Path Algorithm Consider the following maximum flow problem. (Are capacities are shown.) (a) Apply the Ford-Fulkerson algorithm to find a maximum s-t flow. Use the maximum capacity augmenting path method to chose the aug. menting path in each iteration. In the case of a tie, break ties lexico graphically, 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