# Testing optimality via complementary slackness

1. Jul 25, 2011

### zfolwick

I can't for the life of me understand this topic. given a point x =(1,1,1,1,1,1,1) and a primal LP, does the point solve the primal? An internet search revealed no answer to my question, only criteria which involves knowing y. I am aware that $\sum$aijxj < b then yi = 0, so I at least know which elements of y are zero, but the rest of the steps elude me.

2. Jul 25, 2011

### lavinia

you need to be more clear. Explain in more detail.

3. Jul 25, 2011

### zfolwick

given a point x =(a1, a2, ... am), is this point optimal for a given LP?

Is there a good, step-by-step description of this somewhere? The only thing I can find is that, if I have a point x and a point y, then I can use the weak duality theorem to say that cx = by or some such nonsense.

what I'm really trying to understand is the pivoting process wherein I *get* y from a given point x.