Re: Visualizing 3D LP-problems

• To: mathgroup at smc.vnet.net
• Subject: [mg15459] Re: [mg15424] Visualizing 3D LP-problems
• From: Sergio Terrazas <sterraza at campus.cdj.itesm.mx>
• Date: Mon, 18 Jan 1999 04:22:00 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Bjorn!
Hi have done this using a package from mathsource :

Vertex Enumeration for Convex Polytopes
and Arrangements

Version 0.41 Beta
November 14, 1992

Komei Fukuda and Ichiro Mizukoshi

use my notebook if you want. You are welcome to it, although the
explanations are in Spanish.

Sergio Terrazas
Juarez, Mexico

At 08:57 PM 1/13/99 -0500, you wrote:
>Visualizing 3D LP-problems
>
>I want to be able to visualize 3D LP-problems (when lecturing to
>beginners) in a more striking way than by pointing to a corner of the
>lecture room, saying that the floor can be seen as the xy-plane, the
>vertical line where the walls meet is the z-axis, and then going on
>about stretching imaginary pieces of cloth between points on these axes
>to span the feasible region.
>
>*  It should possible to have Mathematica display the convex polyhedron
>that is the boundary of the feasible region of a three variable
>LP-problem (linear programming problem).
>
>*  It would then be nice to be able to rotate the polyhedron, to turn it
>around in various ways so as to get a good feel for what it looks like,
>where the corner points are etc.
>
>*  It would then also be possible to have Mathematica display the
>objective function (a plane) travelling (animation!) towards and
>eventually reaching the desired extreme value (max/min) as it passes
>through the optimal corner point(s) just before leaving/entering the
>feasible region.
>
>I'm still a beginner at Mathematica and this is the next thing I want to
>use it for. In two dimensions I know how to do it and I have seen it
>done by others. In three dimensions, however, I do not (yet) know how to
>do it, nor have I been able to find it done by others. Have you?
>
>Any suggestions, clues, references are welcome.
>
>Regards,
>Bjorn Leonardz
><cblz at hhs.se>
>
>
>Dr. Bjorn Leonardz
>Associate Professor
>Stockholm School of Economics
>http://www.hhs.se
>
>
>
>
>

```

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