Simplex Algorithm

[Albert Chan]

(11-13-2023 05:34 PM)ftneek Wrote:  Proper standard form arguments for Example 3.7.2:
> simplex2([[1,2,0,1,1,0,0,20],[2,1,1,0,0,1,0,10],[-1,4,-2,3,0,0,1,40],[1,4,3,2,0,0,0,0],[0,0,0,0,1,1,1,0]],{5,6,7},7,3,0)

[35,[5,0,0,15,0,0,0],[[1,1/2,1/2,0,3/4,0,-1/4,5],[0,0,0,0,-3/2,1,1/2,0],[0,3/2,-1/2,1,1/4,0,1/4,15],[0,1/2,7/2,0,-5/4,0,-1/4,-35]]]

You can do this with simplex_le too, but not much typing is saved.
Constraints already are "=", artificial variables need to start with -1, thus result negated.

> simplex_le([[1,2,0,1,-1,0,0,20],[2,1,1,0,0,-1,0,10],[-1,4,-2,3,0,0,-1,40],[1,4,3,2,0,0,0,0]],-3)

[35,[5,0,0,15,0,0,0],[[0,3/2,-1/2,1,-1/4,0,-1/4,15],[0,0,0,0,-3/2,1,1/2,0],[1,1/2,1/2,0,-3/4,0,1/4,5],[0,1/2,7/2,0,5/4,0,1/4,-35]]]

Inside numbers not quite match, because simplex_le use pivots order {5,6,1}. But that shouldn't matter.