Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A truck must deliver furniture to stores located in five different cities A, B, C, D, and E. The truck must start and end its root at a period the time (in hours) for travel between the cities is given in the figure below. Find an optimal tour for those traveling salesman problem and give its cost in hours. (Hint: the edge AD is part of an optimal tour.) E Tour: +8 D 46 C Cost in hours: B

A truck must deliver furniture to stores located in five different cities A, B, C, D, and E. The truck must start and end its root at a period the time (in hours) for travel between the cities is given in the figure below. Find an optimal tour for those traveling salesman problem and give its cost in hours. (Hint: the edge AD is part of an optimal tour.) E Tour: +8 D 46 C Cost in hours: B

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 3SC: In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175...
See similar textbooks
icon
Related questions
Question
### Traveling Salesman Problem for Furniture Delivery A truck must deliver furniture to stores located in five different cities: A, B, C, D, and E. The truck must start and end its route at city A. The time (in hours) for travel between the cities is given in the figure below. The objective is to find an optimal tour (the shortest possible route) for this traveling salesman problem and provide its cost in hours. As a hint, it is noted that the edge AD is part of an optimal tour. ### Graph Representation: In the figure, each node represents a city and each edge represents the travel time in hours between two cities. Here is the detailed travel time between each pair of cities: - **A to B:** 35 hours - **A to C:** 40 hours - **A to D:** 22 hours - **A to E:** 18 hours - **B to C:** 29 hours - **B to D:** 21 hours - **B to E:** 18 hours - **C to D:** 25 hours - **C to E:** 32 hours - **D to E:** 23 hours ### Task: Determine the optimal tour starting and ending at city A and the total cost in hours for this tour. #### Input Required: - **Tour:** A sequence of cities representing the optimal route. - **Cost in hours:** The total travel time for the optimal route. This problem is an example of the Traveling Salesman Problem (TSP), where the goal is to find the shortest possible route that visits each city exactly once and returns to the starting city. Solving this will give the optimal sequence for the truck's delivery route along with the minimum total travel time.
Transcribed Image Text:### Traveling Salesman Problem for Furniture Delivery A truck must deliver furniture to stores located in five different cities: A, B, C, D, and E. The truck must start and end its route at city A. The time (in hours) for travel between the cities is given in the figure below. The objective is to find an optimal tour (the shortest possible route) for this traveling salesman problem and provide its cost in hours. As a hint, it is noted that the edge AD is part of an optimal tour. ### Graph Representation: In the figure, each node represents a city and each edge represents the travel time in hours between two cities. Here is the detailed travel time between each pair of cities: - **A to B:** 35 hours - **A to C:** 40 hours - **A to D:** 22 hours - **A to E:** 18 hours - **B to C:** 29 hours - **B to D:** 21 hours - **B to E:** 18 hours - **C to D:** 25 hours - **C to E:** 32 hours - **D to E:** 23 hours ### Task: Determine the optimal tour starting and ending at city A and the total cost in hours for this tour. #### Input Required: - **Tour:** A sequence of cities representing the optimal route. - **Cost in hours:** The total travel time for the optimal route. This problem is an example of the Traveling Salesman Problem (TSP), where the goal is to find the shortest possible route that visits each city exactly once and returns to the starting city. Solving this will give the optimal sequence for the truck's delivery route along with the minimum total travel time.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS