At present, $40,000$ long$-$distance calls must be routed from New York to Los Angeles $($L$.$A$.),$ and $30,000$ calls must be routed from Philadelphia to L$.$A$.$ On route to L$.$A$.$ from Philadelphia or New York, calls are sent through Indianapolis or Cleveland, then through Dallas or Denver, and finally to L$.$A$.$ The number of calls that can be routed between any pair of cities is shown in the attached file phone$\_$calls.xlsx$.$ The phone company wants to know how many of the $70,000$ calls originating in New York and Philadelphia can be routed to L$.$A$.$ Set this up as a network flow model$$that is$,$ specify the nodes, arcs, shipping costs, and arc capacities. Then solve it$.$ You must include the visual network flow model and the essential components of an optimal solution in your submission $($including a Word$/$pdf file and the $.$ipynb file$).$