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: 46

Answer

Using the Brute Force Method, we can see that the shortest route to run errands and return home is 15 miles.
1514432059

Work Step by Step

If we start and end at home, there are 6 possible routes we can take. We can find the total weight of each route. The route is Home, Bank, Post Office, Market, Home. total weight = 3 + 4 + 4.5 + 3.5 = 15 The distance of this route is 15 miles. The route is Home, Bank, Market, Post Office, Home. total weight = 3 + 5 + 4.5 + 5.5 = 18 The distance of this route is 18 miles. The route is Home, Market, Post Office, Bank, Home. total weight = 3.5 + 4.5 + 4 + 3 = 15 The distance of this route is 15 miles. The route is Home, Market, Bank, Post Office, Home. total weight = 3.5 + 5 + 4 + 5.5 = 18 The distance of this route is 18 miles. The route is Home, Post Office, Market, Bank, Home. total weight = 5.5 + 4.5 + 5 + 3 = 18 The distance of this route is 18 miles. The route is Home, Post Office, Bank, Market, Home. total weight = 5.5 + 4 + 5 + 3.5 = 18 The distance of this route is 18 miles. Using the Brute Force Method, we can see that the shortest route to run errands and return home is 15 miles.
Small 1514432059
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.