A certain telephone company would like to determine the maximum number of long-distance calls from Westburgh to Eastville that it can handle at any one time. The company has cables linking these cities via several intermediary cities as follows: Northgate 2 4 Northbay Westburgh (1 3 2 9 6 Eastville 3 Southgate 6 Southbay Each cable can handle a maximum number of calls simultaneously as indicated in the figure. For example, the number of calls routed from Westburgh to Northgate cannot exceed five at any one time. A call from Westburgh to Eastville can be routed through any other city, as long as there is a cable available that is not currently being used to its capacity. In addition to determining the maximum number of calls from Westburgh to Eastville, the company would, of course, like to know the optimal routing of these calls. Assume calls can be routed only in the directions indicated by the arrows. (a) Formulate the above problem as a linear programming problem with upper bounds. (Hint: Denote by xij the number of calls routed from city i to city j.) (b) Find the solution by inspection of the graph.