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Grey Construction Case Study: Minimizing Cable Distance

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12-23) Grey Construction would like to determine the least expensive way of connecting houses it is building with cable TV. It has identified 11 possible branches or routes that could be used to connect the houses. The cost in hundreds of dollars and the branches are summarized in the following table.
(a) What is the least expensive way to run cable to the houses?

Branch Start Node End Node Cost ($100)
Branch 1 1 2 5
Branch 2 1 3 6
Branch 3 1 4 6
Branch 4 1 5 5
Branch 5 2 6 7
Branch 6 3 7 5
Branch 7 4 7 7
Branch 8 5 8 4
Branch 9 6 7 1
Branch 10 7 9 6
Branch 11 8 9 2

(b) After reviewing cable and installation costs, Grey Construction would like to alter the costs for installing cable TV between its houses. The changes are summarized in the following table. What is the impact on total costs?

Branch Start Node End Node Cost ($100)
Branch 1 1 2 5
Branch 2 1 3 1
Branch 3 1 4 1
Branch 4 1 5 1
Branch 5 2 6 7
Branch 6 3 7 5
Branch 7 4 7 7
Branch 8 5 8 4
Branch 9 6 7 1
Branch 10 7 9 6
Branch 11 8 9 2

12-29) Use the shortest route algorithm to determine the minimum distance form node 1 to node 7 in figure below. Which nodes are included in this routes?

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