OPERATION RESEARCH -> SHORTEST PATH + MINIMUM SPANNING TREE . show all your work
ID: 1721595 • Letter: O
Question
OPERATION RESEARCH -> SHORTEST PATH + MINIMUM SPANNING TREE . show all your work in a paper plz
A truck must travel from New York to Los Angeles. As shown in the diagram below, a variety of routes are available. The number associated with each arc is the number of gallons of fuel required by the truck to travel to that city. Use the shortest-path algorithm to find the route from New York to Los Angeles that used the minimum amount of gas. Disregarding the directional arrows in the diagram of #2, use the algorithm for the minimum spanning tree to connect all ovals (nodes) together.Explanation / Answer
Solution : 2
The best route is New York - St. Louis - Phoenix - Los Angeles.
Traveling from New York to Los Angeles Range names used : Dests =Model!$B$16:$B$29 Labeling of nodes Flows =Model!$D$16:$D$29 City Index Gallons =Model!$C$16:$C$29 New York 1 NetFlows =Model!$G$16:$G$23 Cleveland 2 Origins =Model!$A$16:$A$29 St. Louis 3 Reqd =Model!$I$16:$I$23 Nashville 4 TotGallons =Model!$B$31 Phoenix 5 Dallas 6 Salt Lake City 7 Los Angeles 8 Network formulation Node balance constraints Origin Destination Gallons Flow Node Net inflow/outflow Required 1 2 400 0 1 1 = 1 1 3 950 1 2 0 = 0 1 4 800 0 3 0 = 0 2 5 1800 0 4 0 = 0 2 6 900 0 5 0 = 0 3 5 1100 1 6 0 = 0 3 6 600 0 7 0 = 0 4 6 600 0 8 1 = 1 4 7 1200 0 5 8 400 1 6 5 900 0 6 7 1000 0 6 8 1300 0 7 8 600 0 Gallons used : 2450The best route is New York - St. Louis - Phoenix - Los Angeles.
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