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Fort Worth Plano Mesquite Arlington Plano 54 Mesquite 52 38 Arlington 19 53 43 Denton 42 41 56 50

Fort Worth Plano Mesquite Arlington Plano 54 Mesquite 52 38 Arlington 19 53 43 Denton 42 41 56 50

Advanced Engineering Mathematics
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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**Problem Statement:** A company needs to deliver products to each of their 5 stores in the Dallas area. Driving distances are shown in the table below. Use any system you prefer to find a route for the driver to leave Fort Worth, visit each of the stores, and then return to Fort Worth. | | Plano | Mesquite | Arlington | Denton | |------------|-------|----------|-----------|--------| | Fort Worth | 54 | 52 | 19 | 42 | | Plano | | 38 | 53 | 41 | | Mesquite | | | 43 | 56 | | Arlington | | | | 50 | **Explanation of the Table:** - The table represents driving distances between various cities: Fort Worth, Plano, Mesquite, Arlington, and Denton. - Each cell in the table shows the distance (in miles) between two cities. - The diagonal from top-left to bottom-right is not filled as these represent the cities themselves (distance of zero). - Use the given distances to determine a route that efficiently visits each location starting and ending at Fort Worth.
Transcribed Image Text:**Problem Statement:** A company needs to deliver products to each of their 5 stores in the Dallas area. Driving distances are shown in the table below. Use any system you prefer to find a route for the driver to leave Fort Worth, visit each of the stores, and then return to Fort Worth. | | Plano | Mesquite | Arlington | Denton | |------------|-------|----------|-----------|--------| | Fort Worth | 54 | 52 | 19 | 42 | | Plano | | 38 | 53 | 41 | | Mesquite | | | 43 | 56 | | Arlington | | | | 50 | **Explanation of the Table:** - The table represents driving distances between various cities: Fort Worth, Plano, Mesquite, Arlington, and Denton. - Each cell in the table shows the distance (in miles) between two cities. - The diagonal from top-left to bottom-right is not filled as these represent the cities themselves (distance of zero). - Use the given distances to determine a route that efficiently visits each location starting and ending at Fort Worth.
Expert Solution
Step 1: Transforming the problem into standard Travelling salesman problem
  Forth Worth Plano Mesquite Arlington Denton
Forth Worth ∞ 54 52 19 42
Plano 54 ∞ 38 53 41
Mesquite 52 38 ∞ 43 56
Arlington 19 53 43 ∞ 50
Denton 42 41 56 50 ∞
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