Answer to November 29, 2004 Problem |
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The Pleacher Family Travel Problem |
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Mr. Pleacher and his wife want to take a trip to visit his brother, his parents, and each
of their children. Mr. Pleacher and his wife live in Stephens City, VA. (SC on the map below) Mr. Pleacher's brother lives in Leitchfield, KY. (L on the map) Mr. Pleacher's parents live in Owensboro, KY. (O on the map) Mr. Pleacher's daughter Elizabeth and her family live in Ponte Vedra Beach, FL. (PVB on the map) Mr. Pleacher's daughter Sarah and her family live in Fort Collins, CO. (FC on the map) Mr. Pleacher's son Michael and his wife live in Portland, ME. (P on the map) The distances between the cities are given below:
Using the data above, help Mr. Pleacher and his wife plan a roundtrip to visit each relative
without passing through any city more than once (except the return home to Stephens City). |
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Solution to the Problem:
The shortest paths are:
I used a tree diagram to examine all possible paths. Then I set up a
table to find the shortest path(s).
So, paths #2 and #8 above have the least mileage of 5,483 miles,
a savings of 1,101 miles over routes #5 or 12.
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1. John Funk | Ventura, California |
2. Henry Woodward | Columbus, Georgia |
3. Jasmine Gonzalez and Leanna Thammavongsa | Charlton, Massachussetts |
4. Trey Mason | Winchester, Virginia |
5. Sharina Broughton | Old Dominion University, Norfolk, Virginia |
6. Per Björkil | Tullängskolan, Örebro, Sweden |
7. Viktor Logrell | Tullängskolan, Örebro, Sweden |
8. Bahadir Güngör | Tullängskolan, Örebro of Sweden |
9. Jonas Sutinen | Tullängsskolan, Örebro, Sweden |
10. Gustav Nilsson | Tullängsskolan, Örebro, Sweden |
11. Jim Kennedy | Limerick, Ireland |
12. Nate Troup | Arlington, Virginia |
13. David & Judy Dixon | Bennettsville, South Carolina |
14. Jeffrey Gaither | Winchester, Virginia |
15. Jonathan Haxxor | Tullängskolans, Örebro, Sweden |
16. Daniel Kvist | Tullängskolan, Örebro, Sweden |
17. Erik Hultgren | Tullängskolan, Örebro, Sweden |
18. James Alarie | University of Michigan -- Flint, Flint, Michigan |
19. Erik Ekman | Tullängskolan, Örebro, Sweden |
20. Clay Thomas | ---------- |
21. Cameron S. | Columbus, Georgia |
22 Ann Norman | Columbus, Georgia |
23. Anders Johansson | Tullängsskolan, Örebro, Sweden |
24. Linda Axelsson | Tullängsskolan, Örebro, Sweden |
25. Joanna Sturk | Tullängsskolan, Örebro, Sweden |
26. Stehr Ako | Tullängskolan, Örebro, Sweden |