When installing fiber optics, some companies will install a sonet ring; a full loop of cable connecting multiple locations. This is used so that if any part of the cable is damaged it does not interrupt service, since there is a second connection to the hub. A company has 5 buildings. Costs (in thousands of dollars) to lay cables between pairs of buildings are shown below. Find the circuit that will minimize cost:
When installing fiber optics, some companies will install a sonet ring; a full loop of cable connecting multiple locations. This is used so that if any part of the cable is damaged it does not interrupt service, since there is a second connection to the hub. A company has 5 buildings. Costs (in thousands of dollars) to lay cables between pairs of buildings are shown below. Find the circuit that will minimize cost:
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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![**Fiber Optic Installation and Cost Optimization**
When installing fiber optics, some companies will establish a sonet ring—a full loop of cable connecting multiple locations. This setup ensures service continuity even if part of the cable is damaged, as there's an alternative connection to the hub. In this scenario, a company has five buildings. The cost (in thousands of dollars) to lay cables between pairs of buildings is illustrated. Your task is to determine the circuit that minimizes cost.
**Diagram Explanation:**
The diagram is a graph consisting of five nodes, labeled A, B, C, D, and E, representing the buildings. Each node is connected by edges, which represent potential cable paths. The numbers on each edge indicate the cable installation cost between the connected buildings:
- A to B: $5.9
- A to C: $5.1
- A to D: $5.6
- A to E: $4.4
- B to C: $6.0
- B to D: $4.3
- B to E: $5.2
- C to D: $4.7
- C to E: $5.1
- D to E: $5.8
**Optimization Methods:**
1. **Using Nearest Neighbor Starting at Building A:**
- Aim to begin at building A and choose the least costly path to visit each building once and return to the start.
2. **Using Sorted Edges (starting with CE...):**
- Sort all edges by cost and choose paths in ascending order, while ensuring a complete circuit is formed without repetition.
**Objective:**
Identify the optimal circuit configuration that incurs the lowest expense while ensuring all buildings are effectively connected. Enter your solutions in the boxes provided:
- Nearest Neighbor route: [ ]
- Sorted Edges route: [ ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08858a66-edac-4fcd-aee1-0f04b5b0ad0e%2Ff78116f2-8012-4be0-8ddb-772850869e2c%2Fu6hpb9l_processed.png&w=3840&q=75)
Transcribed Image Text:**Fiber Optic Installation and Cost Optimization**
When installing fiber optics, some companies will establish a sonet ring—a full loop of cable connecting multiple locations. This setup ensures service continuity even if part of the cable is damaged, as there's an alternative connection to the hub. In this scenario, a company has five buildings. The cost (in thousands of dollars) to lay cables between pairs of buildings is illustrated. Your task is to determine the circuit that minimizes cost.
**Diagram Explanation:**
The diagram is a graph consisting of five nodes, labeled A, B, C, D, and E, representing the buildings. Each node is connected by edges, which represent potential cable paths. The numbers on each edge indicate the cable installation cost between the connected buildings:
- A to B: $5.9
- A to C: $5.1
- A to D: $5.6
- A to E: $4.4
- B to C: $6.0
- B to D: $4.3
- B to E: $5.2
- C to D: $4.7
- C to E: $5.1
- D to E: $5.8
**Optimization Methods:**
1. **Using Nearest Neighbor Starting at Building A:**
- Aim to begin at building A and choose the least costly path to visit each building once and return to the start.
2. **Using Sorted Edges (starting with CE...):**
- Sort all edges by cost and choose paths in ascending order, while ensuring a complete circuit is formed without repetition.
**Objective:**
Identify the optimal circuit configuration that incurs the lowest expense while ensuring all buildings are effectively connected. Enter your solutions in the boxes provided:
- Nearest Neighbor route: [ ]
- Sorted Edges route: [ ]
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