he Ranch Development Project was undertaken by two real estate companies in the Colorado high country and several investors from Oklahoma. The idea was to convert the working ranch into a luxury single-family development. The project became known as The Ranch. The average home price was $475,000, and it was not uncommon to have homes valued at more than $1 million. The center of the development was a first-class 18-hole golf course. Green fees could approach $100 per day, depending on services required. Some have claimed that the course is one of the best in Colorado. The Ranch also had a four-star restaurant located in a beautiful and spacious log cabin, which included a fireplace big enough for a 6-foot-tall person to walk into without hitting his head. Other amenities included a heated pool, lighted tennis courts, and a complete workout center. Free shuttle service was provided to the ski slopes a few miles away. To preserve the beauty of the area and to enhance property values, each home site varied from 1 acre to more than 20 acres. There were numerous building restrictions. Every home and structure had to be approved by the Ranch Development Board. Approval required developing a scale model of all buildings on the property and a complete set of blueprints. The average cost of preparing the necessary plans was $25,000. The concept of a footprint was also used. A footprint is a relatively small circular area on each plot of land. Homes and all structures had to be placed inside the footprint. Although the homeowner held title to the entire property, all structures had to be placed in the footprint unless special permission was given by the Ranch Development Board (a rare occurrence). Each homeowner had to pay monthly fees, depending on the location and value of the land. The fees could vary from $450 to more than $1,250 per month. These fees included water, sewer, cable TV, and access to the pool, tennis courts, and exercise facility. Golf and restaurant fees were additional. One of the developments in The Ranch is outlined in the figure below this problem.  The development was not as close to the golf course as some of the others, but it had a beautiful trout stream and pond in the center. The footprints are shown in the network. Distances between footprints are given in hundreds of feet. Requirements: 1) Determine the least expensive way to connect all the homes with water and sewer lines. Assume that minimizing total distance will also minimize total costs. HINT: Type in the total minimum distance to connect nodes and how the nodes connect.

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The Ranch Development Project was undertaken by two real estate companies in the Colorado high country and several investors from Oklahoma. The idea was to convert the working ranch into a luxury single-family development. The project became known as The Ranch. The average home price was $475,000, and it was not uncommon to have homes valued at more than $1 million. The center of the development was a first-class 18-hole golf course. Green fees could approach $100 per day, depending on services required. Some have claimed that the course is one of the best in Colorado. The Ranch also had a four-star restaurant located in a beautiful and spacious log cabin, which included a fireplace big enough for a 6-foot-tall person to walk into without hitting his head. Other amenities included a heated pool, lighted tennis courts, and a complete workout center. Free shuttle service was provided to the ski slopes a few miles away.

To preserve the beauty of the area and to enhance property values, each home site varied from 1 acre to more than 20 acres. There were numerous building restrictions. Every home and structure had to be approved by the Ranch Development Board. Approval required developing a scale model of all buildings on the property and a complete set of blueprints. The average cost of preparing the necessary plans was $25,000. The concept of a footprint was also used. A footprint is a relatively small circular area on each plot of land. Homes and all structures had to be placed inside the footprint. Although the homeowner held title to the entire property, all structures had to be placed in the footprint unless special permission was given by the Ranch Development Board (a rare occurrence).

Each homeowner had to pay monthly fees, depending on the location and value of the land. The fees could vary from $450 to more than $1,250 per month. These fees included water, sewer, cable TV, and access to the pool, tennis courts, and exercise facility. Golf and restaurant fees were additional.

One of the developments in The Ranch is outlined in the figure below this problem.  The development was not as close to the golf course as some of the others, but it had a beautiful trout stream and pond in the center. The footprints are shown in the network. Distances between footprints are given in hundreds of feet.

Requirements:

1) Determine the least expensive way to connect all the homes with water and sewer lines. Assume that minimizing total distance will also minimize total costs.

  • HINT: Type in the total minimum distance to connect nodes and how the nodes connect. 
The image is a map illustrating a network of nodes and pathways, typically used for graph theory or network topology studies. The nodes are numbered from 1 to 27, and the connections between nodes have designated weights, represented by numbers along each connecting line, indicating the distance or cost associated with each path.

A pond and two streams are depicted on the map:

1. **Pond**: At the center of the network, there is a pond, surrounded by nodes 10, 15, 16, and 22.

2. **Streams**: Two streams are illustrated:
   - One stream flows between nodes 13 and 15.
   - Another stream intersects between nodes 22 and 23.

**Nodes and Connections**:

- **Node 1 to Node 2**: The connection has a weight of 5.
- **Node 2 to Node 3**: The connection has a weight of 6.
- **Continuing around the network**, connections vary in weight, ranging from 1 to 11.

The structure forms a complex network featuring various cycles and paths, allowing for the exploration of shortest path algorithms, network flow analysis, or optimization problems. The presence of the pond and streams adds a geographical element that might represent obstacles or areas of interest impacting the network's traversal costs.
Transcribed Image Text:The image is a map illustrating a network of nodes and pathways, typically used for graph theory or network topology studies. The nodes are numbered from 1 to 27, and the connections between nodes have designated weights, represented by numbers along each connecting line, indicating the distance or cost associated with each path. A pond and two streams are depicted on the map: 1. **Pond**: At the center of the network, there is a pond, surrounded by nodes 10, 15, 16, and 22. 2. **Streams**: Two streams are illustrated: - One stream flows between nodes 13 and 15. - Another stream intersects between nodes 22 and 23. **Nodes and Connections**: - **Node 1 to Node 2**: The connection has a weight of 5. - **Node 2 to Node 3**: The connection has a weight of 6. - **Continuing around the network**, connections vary in weight, ranging from 1 to 11. The structure forms a complex network featuring various cycles and paths, allowing for the exploration of shortest path algorithms, network flow analysis, or optimization problems. The presence of the pond and streams adds a geographical element that might represent obstacles or areas of interest impacting the network's traversal costs.
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