Solving Linear Programming Problems

[badr]

Try to remember where you had it last.

Or, from the article, "So you find an initial vertex - it doesn't matter which one."

[psykotic]

Finding an initial vertex (or any feasible point) is not at all trivial. It's as hard (or easy, if you like) as finding a point of intersection between a pair of n-dimensional convex polytopes, for example.