# Given the following network, what is the shortest route?

3) Given the following network, what is the shortest route?

From To Distance (Km)

1 2 7

1 3 9

1 4 18

2 3 3

3 2 3

3 5 4

5 3 4

2 5 5

5 2 5

4 6 3

5 6 2

6 5 2

5 7 6

6 7 3

https://brainmass.com/physics/atomic-and-molecular-physics/following-network-shortest-route-277646

#### Solution Summary

The expert determines the shortest route given a network.

Solutions to Network Model problems related to Cost Minimization, and Shortest route algorithm are given with step by step explanation in easy to understand language.

Solutions to Network Model problems related to Cost Minimization, and Shortest route algorithm are given with step by step explanation in easy to understand language. Please see the problems if you need solutions to such type of problems. I assure, if you need solutions to such type of problems, you can use these solutions as model to solve your own problems.

Problem (1)

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.

Branch Sart 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

Problem (2)

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 Sart 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

Problem (3):

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?