Consider the minimum cost flow problem shown below, where the $b_i$ values are given by the nodes, the $c_{ij}$ values are given by the arcs, and the finite $u_{ij}$ values are given in parentheses by the arcs. The remaining upper bounds are infinite. Obtain an initial basic feasible solution $($bfs$)$ with basic arcs $AC,BA,CD,$ and $CE.($The number of goods transferred is not given, so based on the bfs you need to determine the amount transferred$).$ Did the solution you find optimal? If not, determine entering and leaving variables and the value of $.$ Then, show new basic and nonbasic variables.