The following example illustrates the solution methods for the shortest route and minimal spanning tree network flow problems.
A salesman for Healthproof Pharmaceutical Company travels each week from his office in Atlanta to one of five cities in the Southeast where he has clients . The travel time (in hours) between cities along interstate highways is shown along each branch in the following network:
Determine the shortest route from Atlanta to each of the other five cities in the network.
Assume that the network now represents six different communities in a city and that the local transportation authority wants to design a rail system that will connect all six communities with the minimum amount of track. The miles between each community are shown on each branch. Develop a minimal spanning tree for this problem.
Step 1.  (Part A): Determine the Shortest Route Solution
The shortest route network follows :
 
Step 2.  (Part B): Determine the Minimal Spanning Tree
