Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 3

In 1861, Western Union wanted to develop a transcontinental telegraph network to connect all the forts and trading posts from St. Louis to Oregon that are shown on the network, in problem, which had grown into communities. Multiplying the days shown on the network by 10 as a rough estimate of the miles between each node, develop a minimal spanning tree for this network that connects the different communities with the minimum amount of telegraph line.
Problem
From 1840 to 1850, more than 12,000 pioneers migrated west in wagon trains. It was typically about a 2,000-mile journey, and pioneers averaged about 10 miles per day. One pioneer family, the Smiths, is planning to join a wagon train traveling west to Oregon. The destination is Fort Vancouver, which is near present-day Portland. The family plans to join a wagon train in St. Louis. However, the trains follow various trails west that are mostly determined by the location of forts and trading posts along the way. The Smith family wants to choose a wagon train that will get them to Oregon in the shortest amount of time. They have checked around with the different wagon train leaders plus immigrants, soldiers, fur traders, and scouts who have previously made the trip west, and from the information they have gathered, they have developed the following network, with estimated times (in days) along each branch:

a. Determine the shortest route for the Smiths from St. Louis to Ft. Vancouver.
b. Another family, the Steins, is leaving from Ft. Smith, Arkansas. Determine the shortest route for the Steins to Ft. Vancouver, Oregon.