Reconsider Prob. 9.3-1. Now formulate this problem as a minimum cost flow problem by showing the appropriate network representation.

Prob. 9.3-1

You need to take a trip by car to another town that you have never visited before. Therefore, you are studying a map to determine the shortest route to your destination. Depending on which route you choose, there are five other towns (call them A, B, C, D, E) that you might pass through on the way. The map shows the mileage along each road that directly connects two towns without any intervening towns. These numbers are summarized in the following table, where a dash indicates that there is no road directly connecting these two towns without going through any other towns.

(a) Formulate this problem as a shortest-path problem by drawing a network where nodes represent towns, links represent roads, and numbers indicate the length of each link in miles.

(b) Use the algorithm described in Sec. 9.3 to solve this shortestpath problem.

(c) Formulate and solve a spreadsheet model for this problem.

(d) If each number in the table represented your cost (in dollars) for driving your car from one town to the next, would the answer in part (b) or (c) now give your minimum cost route?

(e) If each number in the table represented your time (in minutes) for driving your car from one town to the next, would the answer in part (b) or (c) now give your minimum time route?