Visualizing 3D LP-problems

• To: mathgroup at smc.vnet.net
• Subject: [mg15424] Visualizing 3D LP-problems
• From: Bjorn <Bjorn.Leonardz at hhs.se>
• Date: Wed, 13 Jan 1999 20:57:36 -0500
• Organization: Stockholm School of Economics
• Sender: owner-wri-mathgroup at wolfram.com

```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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