Consider the weighted undirected bipartite graph $G_2=(V_2,E_2)$ given in Figure $2.$

Figure $2$: The weighted undirected bipartite graph $G_2.$

$($a$)$ Use the iterative shortest path algorithm to find a maximum weight matching in the graph $G_2.$ For each iteration of the algorithm, report the following:

the current matching and its weight;

the corresponding auxiliary graph; and

the augmenting path used to update the matching $($if one exists$).$