HW10_Sol - include Dallas-St. Louis(length 600). Next...

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E160 Operations Research I Fall 2008 Homework #10 Solution Chapter 8 Section 8.6 1. We begin at Gary and include the Gary-South Bend arc. Then we add the South Bend-Fort Wayne arc. Next we add the Gary-Terre Haute arc. Finally we add the Terre Haute-Evansville arc. This minimum spanning tree has a total length of 58 + 79 + 164 + 113 = 414 miles. 2. We begin at node 1 with arc (1,3). Then we add (in turn) arcs (3,5), arc (3,4), and arc (3,2). Total length of the tree is 15. Review Problem 5. Begin at NY and include NY-Cleveland arc (length 400). Next include NY-Nashville arc (length 800). Next include Nashville-Dallas(length 600). Next
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Unformatted text preview: include Dallas-St. Louis(length 600). Next include Dallas-Phoenix(length 900). Next include Phoenix-LA (length 400. Finally include Salt Lake City-Los Angeles (length 600). Total length of minimum spanning tree is 4300 miles. 4. Solution: First we can find the minimum spanning tree of the graph: Add edges (1,2), (10,11), (9,12), (11,12), (8,11), (4,5), (6,9), (1,4), (3,6), (5,8), (7,10) in turn, we get a minimum spanning tree. So, since the unique path given by the minimum spanning tree is a minmax path of the pair of node. So, the path from node 1 to node 12, minimize the maximum altitude is 1->4->5->8->11->12....
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