**Network Connection Problem in a Youth Camp****Problem Statement:**Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility.**Diagram Explanation:**The network diagram consists of seven nodes labeled A, B, C, D, E, F, and G. Lines (edges) connect these nodes, representing potential paths between facilities. Each edge is marked with a numerical value indicating the distance between the two connected facilities in tens of yards.- The distance between nodes A and C is 9.- The distance between nodes A and B is 40.- The distance between nodes A and D is 11.- The distance between nodes A and E is 7.- The distance between nodes C and E is 12.- The distance between nodes C and F is 10.- The distance between nodes E and F is 9.- The distance between nodes E and G is 10.- The distance between nodes E and D is 8.- The distance between nodes D and B is 20.- The distance between nodes D and G is 15.- The distance between nodes B and G is 8.- The distance between nodes F and G is 20.**Task:**Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize construction time and cost), the directors want to determine which paths should be constructed. Use this network to determine which paths should be built. (Hint: find the minimal spanning tree). You need to show your algorithm progress step by step.---**Steps to Find the Minimal Spanning Tree:**1. **List all edges/weights and sort by weight**: Sort edges in ascending order of distances.2. **Choose the edge with the smallest weight**: Ensure it doesn't form a cycle with the edges already selected.3. **Repeat until all nodes are connected**: Continue adding edges with the smallest weight until every facility is connected with minimal total distance.This problem will help in understanding algorithms related to network theory, particularly about constructing a minimal spanning tree, which is crucial for optimizing paths and resource use.

4- Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. 10 12 A 20 40 10 20 15 B G Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should

4- Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. 10 12 A 20 40 10 20 15 B G Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should

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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**Network Connection Problem in a Youth Camp**

**Problem Statement:**

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility.

**Diagram Explanation:**

The network diagram consists of seven nodes labeled A, B, C, D, E, F, and G. Lines (edges) connect these nodes, representing potential paths between facilities. Each edge is marked with a numerical value indicating the distance between the two connected facilities in tens of yards.

- The distance between nodes A and C is 9.
- The distance between nodes A and B is 40.
- The distance between nodes A and D is 11.
- The distance between nodes A and E is 7.
- The distance between nodes C and E is 12.
- The distance between nodes C and F is 10.
- The distance between nodes E and F is 9.
- The distance between nodes E and G is 10.
- The distance between nodes E and D is 8.
- The distance between nodes D and B is 20.
- The distance between nodes D and G is 15.
- The distance between nodes B and G is 8.
- The distance between nodes F and G is 20.

**Task:**

Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize construction time and cost), the directors want to determine which paths should be constructed. Use this network to determine which paths should be built. (Hint: find the minimal spanning tree). You need to show your algorithm progress step by step.

---

**Steps to Find the Minimal Spanning Tree:**

1. **List all edges/weights and sort by weight**: Sort edges in ascending order of distances.
2. **Choose the edge with the smallest weight**: Ensure it doesn't form a cycle with the edges already selected.
3. **Repeat until all nodes are connected**: Continue adding edges with the smallest weight until every facility is connected with minimal total distance.

This problem will help in understanding algorithms related to network theory, particularly about constructing a minimal spanning tree, which is crucial for optimizing paths and resource use.

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