Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 14 - Graph Theory - 14.3 Hamilton Paths and Hamilton Circuits - Exercise Set 14.3: 40

Answer

Using the Nearest Neighbor Method, the Hamilton circuit is A,D,E,C,B,A. The total weight of the circuit is 1457. This means that the total cost is $1457.

Work Step by Step

With the Nearest Neighbor Method, we should choose the edge which has the smallest weight for each step along the path. Let's start at vertex A. We can travel along edge AB, AC, AD, or AE. The weights of these paths are 500, 200, 185, and 205, respectively. We should travel along the edge AD because it has the smallest weight. From vertex D, we can travel along edge DB, DC, or DE. The weights of these paths are 360, 320, and 302, respectively. We should travel along edge DE because it has the smallest weight. From vertex E, we can travel along edge EB or EC. The weights of these paths are 340 and 165, respectively. We should travel along edge EC because it has the smallest weight. From vertex C, the path must travel to vertex B, and then finally back to vertex A to complete the Hamilton circuit. Using the Nearest Neighbor Method, the Hamilton circuit is A,D,E,C,B,A. The edges in this path are AD, DE, EC, CB, and BA. The weights of these edges are 185, 302, 165, 305, and 500. We can find the total weight of this Hamilton circuit. total weight = 185 + 302 + 165 + 305 + 500 total weight = 1457 Using the Nearest Neighbor Method, the Hamilton circuit is A,D,E,C,B,A. The total weight of the circuit is 1457. This means that the total cost is $1457.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.