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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

811.0. "Family Get-Together" by LABC::FRIEDMAN () Tue Jan 05 1988 17:56

    A family whose members live in different cities wants to get
    together at a restaurant in a "central" location, that is,
    a location that minimizes the sums of the distances each
    family member would have to travel.  How would you go about
    solving this problem mathematically?
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811.1. . .KEEPER::KOSTASHe is great who confers the most benefits.Tue Jan 05 1988 18:297
    re. .0
    
    Well, 
         they wont have to travel far if any of these family members
    are relatives of the traveling salesman.

    /k
811.2Give that man the third degreeSQM::HALLYBKhan or bust!Wed Jan 06 1988 14:334
    ... and is this easier or harder than minimizing travel _costs_?
    What if there's no restaurant at the minimum-distance point?
    Or are there a finite number of restaurants to choose from?  
    If so, where are they?
811.3LABC::FRIEDMANThu Jan 07 1988 14:443
    After finding the minimum-distance point, the closest restaurant
    will be chosen, so the problem is merely to find the minimum-distance
    point.
811.4Who needs digital computers?AKQJ10::YARBROUGHWhy is computing so labor intensive?Thu Jan 07 1988 15:0614
There is a cute analog solution to this problem. Get yourself a map  (a 
Mercator projection map may not be good enough; the distances and angles 
must both be reasonably accurate) and a piece of flat metal or plastic of 
the same size. Drill holes in the material corresponding to people's homes 
on the map. Through the holes pass (equally) weighted threads; tie all the
threads together above the material in a knot, with the weighted ends of 
the threads hanging through the holes. The place on the map where the knot
is stable (won't move away when the whole thing is jiggled) is the point
you seek. 

If it turns out that the knot is stable in several places then you have a
case where any point within the convex hull of the locations will do.

Lynn Yarbrough