Problem 2. The FMU Environmental program was recently given a large plot of land by the Environmental Protection Agency (EPA) to conduct a habitat sustainability study. The EPA constructed twelve small dwelling on the land in different locations. The objective of the study was to use twelve different recycling techniques to see which one was best suited for sustainable human habitation. To reduce the impact of isolation on the test subjects, FMU was required to construct a walking path that connects all twelve dwellings. The study director wants to determine the best way to connect all the dwellings in order to keep the total distance as low as possible. You have been given the assignment to find the minimal distance necessary to connect all the dwellings (see graph for Problem 2). a. Determine the minimal spanning tree for the dwellings. b. What is the total distance of all the paths between the habitats? c. What is the shortest distance from habitat 1 to habitat 10?

Problem 2 - Graph 80 6 11 110 2 35 60 8 50 55 45 55 4 110 30 160 70 10 1 25 50 7 75 25 50 5 45 75 55 65 25 12 140 60