Testing optimality via complementary slackness

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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 \sumaijxj < b then yi = 0, so I at least know which elements of y are zero, but the rest of the steps elude me.
 
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zfolwick said:
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 \sumaijxj < b then yi = 0, so I at least know which elements of y are zero, but the rest of the steps elude me.

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

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