I know the straightforward graphical solution is possible only for 2 variable problems (unless you have a 3-d graph paper). However, is there some hack to solve a 3 var problem graphically - i.e. convert it into 2 smaller problems and merge back or something like that?
asked
Gen |

it is not possible with one projection. think of the polytope of feasible solutions e.g., as the unit cube. if you project this down to 2d (that is, a plane) you will lose some information because several (in this case: two) extreme points are projected to the same coordinates in the plane. without further knowledge you cannot recover the original coordinates of the solution you end up with. It would be nice, however, to see an applet for your "3d paper".
answered
Marco Luebbecke ♦ |

You can solve a three-variable problem graphically using computer software, specifically something that can (a) draw and possibly shade 3-d polygons and (b) rotate the viewpoint. Mathematica, for instance, can do that. You can also use analog methods by modeling the feasible region with some combination of modeler's clay, wooden dowels, stiff paper/plastic, cardboard, ... (Some of us are old enough to remember the analog days. Right, Mike?) Combining those two approaches, you could buy one of the new 3D printers and program to generate a solid representation of the feasible region.
answered
Paul Rubin ♦♦ |