Transport, allocation, and networks.Case 1.A company wants to reinforce its internal fiber optic network by laying new fiber between twoof its centers. To do this you want to use the existing pipes, which have the lengths indicated inthe following table:FromToLength1 1 1 2 2 2 3 3 3 4 4 52 3 5 3 4 6 4 5 6 5 6 64 3 5 13 5 2 2 5 1 1 3You can assume that the arcs indicated in the table are directed.Considering that the cost is proportional to the length of the laying path, find the route with thelowest possible cost that connects 1 with 6. Indicate the pipelines through which one of theoptimal routes passes.Use the appropriate method to solve the problem.Determine the total capacity of the connection between 1 and 6.- Shows the routes necessary to reach the maximum capacity.- The use of software to solve the problem is not allowed.*Please be as clear and legible as possible. Show and explain all the steps. Thank you very much.

Answered: Transport, allocation, and networks.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Transport, allocation, and networks.
Case 1.
A company wants to reinforce its internal fiber optic network by laying new fiber between two
of its centers. To do this you want to use the existing pipes, which have the lengths indicated in
the following table:
From
To
Length
1 1 1 2 2 2 3 3 3 4 4 5
2 3 5 3 4 6 4 5 6 5 6 6
4 3 5 13 5 2 2 5 1 1 3
You can assume that the arcs indicated in the table are directed.
Considering that the cost is proportional to the length of the laying path, find the route with the
lowest possible cost that connects 1 with 6. Indicate the pipelines through which one of the
optimal routes passes.
Use the appropriate method to solve the problem.
Determine the total capacity of the connection between 1 and 6.
- Shows the routes necessary to reach the maximum capacity.
- The use of software to solve the problem is not allowed.
*Please be as clear and legible as possible. Show and explain all the steps. Thank you very much.

Expert Solution

Step 1: Step 1:

To find the route with the lowest possible cost that connects node 1 with node 6 in the internal fiber optic network, you can use the Dijkstra's algorithm. Dijkstra's algorithm is a widely-used method for finding the shortest path in a weighted graph. In this case, the weights are proportional to the length of the laying path.

Here are the steps to solve the problem:

Step 1: Create a table to keep track of the minimum cost and the previous node for each node in the network. Initialize the table as follows:

Node	Minimum Cost	Previous Node
1	0	None
2	∞	None
3	∞	None
4	∞	None
5	∞	None
6	∞	None

Start with node 1 and mark it as the current node.
Update the costs and previous nodes for all nodes adjacent to the current node. The cost to reach an adjacent node is the length of the laying path.
Repeat the above step until all nodes are marked as visited.