Textbook Problem

Maude Jenkins, a 90-year-old woman, is planning to walk across the state, west to east, to gain support for a political cause she favors.⁶ She wants to travel the shortest distance to get from city 1 to city 10, using the arcs (roads) shown in Figure 5.27. The numbers on the arcs are miles. Arcs with double-headed arrows indicate that travel is possible in both directions (with the same distance in both directions). What route should Maude take?

How difficult is it to add nodes and arcs to an existing shortest path model? Answer by adding a new node, node 11, to Maude’s network. Assume that node 11 is at the top of the network, geographically, with double- arrowed arcs joining it to nodes 2, 5, and 7 with distances 45, 22, and 10. Assume that Maude’s objective is still to get from node 1 to node 10. Does the new optimal solution go through node 11?