Question Sarah and Jennifer have just graduated from college at the University of Washington in Seattle and want to go on a road trip. They have always wanted to see the mile-high city of Denver. Their road atlas shows the driving time (in hours) between various city pairs, as shown below. Formulate and solve a network optimization model to find the quickest route from Seattle to Denver? Seattle 3 Portland 9 10 Boise Butte 7 Salt Lake City 14 5 12 Grand Junction 4 7 Billings Cheyenne Denver 1

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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**Question**

Sarah and Jennifer have just graduated from college at the University of Washington in Seattle and want to go on a road trip. They have always wanted to see the mile-high city of Denver. Their road atlas shows the driving time (in hours) between various city pairs, as shown below. Formulate and solve a network optimization model to find the quickest route from Seattle to Denver.

**Graph Explanation**

The diagram represents a network of cities connected by roads, with each road labeled by the driving time in hours. The cities included in the network are:

- Seattle
- Portland
- Boise
- Butte
- Billings
- Salt Lake City
- Grand Junction
- Cheyenne
- Denver

The connections and driving times between cities are as follows:

- Seattle to Portland: 3 hours
- Seattle to Boise: 9 hours
- Seattle to Butte: 10 hours
- Portland to Boise: 7 hours
- Boise to Butte: 7 hours
- Boise to Salt Lake City: 6 hours
- Butte to Billings: 4 hours
- Butte to Salt Lake City: 7 hours
- Billings to Cheyenne: 7 hours
- Billings to Denver: 12 hours
- Salt Lake City to Grand Junction: 5 hours
- Grand Junction to Denver: 4 hours
- Salt Lake City to Cheyenne: 7 hours
- Cheyenne to Denver: 1 hour

To solve for the quickest route from Seattle to Denver, you need to apply a network optimization model, such as Dijkstra's algorithm or another shortest path algorithm, and calculate the minimum total driving time.
Transcribed Image Text:**Question** Sarah and Jennifer have just graduated from college at the University of Washington in Seattle and want to go on a road trip. They have always wanted to see the mile-high city of Denver. Their road atlas shows the driving time (in hours) between various city pairs, as shown below. Formulate and solve a network optimization model to find the quickest route from Seattle to Denver. **Graph Explanation** The diagram represents a network of cities connected by roads, with each road labeled by the driving time in hours. The cities included in the network are: - Seattle - Portland - Boise - Butte - Billings - Salt Lake City - Grand Junction - Cheyenne - Denver The connections and driving times between cities are as follows: - Seattle to Portland: 3 hours - Seattle to Boise: 9 hours - Seattle to Butte: 10 hours - Portland to Boise: 7 hours - Boise to Butte: 7 hours - Boise to Salt Lake City: 6 hours - Butte to Billings: 4 hours - Butte to Salt Lake City: 7 hours - Billings to Cheyenne: 7 hours - Billings to Denver: 12 hours - Salt Lake City to Grand Junction: 5 hours - Grand Junction to Denver: 4 hours - Salt Lake City to Cheyenne: 7 hours - Cheyenne to Denver: 1 hour To solve for the quickest route from Seattle to Denver, you need to apply a network optimization model, such as Dijkstra's algorithm or another shortest path algorithm, and calculate the minimum total driving time.
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