Answered: 24. In the original Gorman Construction…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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In the original Gorman Construction Company problem, we found the shortest distance from the office (node 1) to the construction site located at node 6. Because some of the roads are highways and others are city streets, the shortest-distance routes between the office and the construction site may not necessarily provide the quickest or shortest-time route. Shown here is the Gorman road network with travel time rather than distance. Find the shortest route from Gorman’s office to the construction site at node 6 if the objective is to minimize travel time rather than distance.

**Text Transcription:**

24. In the original Gorman Construction Company problem, we found the shortest distance from the office (node 1) to the construction site located at node 6. Because some of the roads are highways and others are city streets, the shortest-distance routes between the office and the construction site may not necessarily provide the quickest or shortest-time route. Shown here is the Gorman road network with travel time rather than distance. Find the shortest route from Gorman’s office to the construction site at node 6 if the objective is to minimize travel time rather than distance.

**Graph/Diagram Explanation:**

The diagram is a network graph with six nodes labeled 1 through 6, representing different locations. Each node is connected by edges, which are labeled with travel times in minutes. The goal is to identify the shortest route, in terms of time, from node 1 to node 6.

Here are the connections and their respective travel times:

- Node 1 is connected to:
- Node 2 with a travel time of 40 minutes
- Node 3 with a travel time of 36 minutes

- Node 2 is connected to:
- Node 3 with a travel time of 6 minutes
- Node 4 with a travel time of 12 minutes
- Node 6 with a travel time of 25 minutes

- Node 3 is connected to:
- Node 4 with a travel time of 15 minutes

- Node 4 is connected to:
- Node 5 with a travel time of 18 minutes
- Node 6 with a travel time of 11 minutes

- Node 5 is connected to:
- Node 6 with a travel time of 23 minutes

The instruction is to find the path from node 1 to node 6 that results in the minimum travel time.

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