Linear Programming: Simplex Method.?

Hi. Simplex means in one direction at a time. Does this help? From the web: "Standard technique in linear programming for solving an optimization problem, typically one involving a function and several constraints expressed as inequalities. The inequalities define a polygonal region (see polygon), and the solution is typically at one of the vertices. The simplex method is a systematic procedure for testing the vertices as possible solutions."

It easiest to understand the simplex method in 2 dimensions.

Assume you have a convex 2 dimensional polygon (this means you can't draw a line from any point on the polygon to another point on the polygon that doesn't either lie along a vertex, or intersect the polygon. A square is a simple version of a convex polygon.

Given a set of constraints for a problem you always get a convex polygon. As an example, you might have a mixture of 100 toyotas, and 50 hondas to sell. Then the total number of cars can be represented as a rectangle 100 (representing the toyotas) and 50 (representing the hondas).

The simplex algorithm relies on the convexity of the polygon. So that given a constraint like that you make $200/honda and $100/toyota. You only have to check the nearest vertices to see if one is bigger than the current one. If it is then that vertex is a better deal (better return on the constraint), and you can continue with the process.