### Traveling Salesman Problem for Furniture DeliveryA 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.

Optimal tour for the truck, if the travel along the diagonal.

Answered: A truck must deliver furniture to…

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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