In the simplex algorithm in linear programming, what are conditions for a variable to leave a basis (not necessarily basis for the/an optimal solution)? I'm supposed to list as many sufficient and necessary conditions as possible for some basic variable \( x_q\) which could be slack, artificial or non-slack and non-artificial.
Well since it's a basic variable, I'm guessing the $x_q$ column already has 0's everywhere except in the s-th row. Now, the $x_q$ row has 0's everywhere in the column of $x_q$ like: This is in the context of the Big M Method and artificial variables. I'm not quite sure what the relationship is exactly, though. What I tried: \(x_q\) leaves if there is some non-basic variable \(x_r\) that enters because
Is that right? Any other sufficient or necessary conditions? What is the relevance of the 0's in the row? Also, how do I approach the last question? I have no clue. asked 07 May '16, 07:21 BCLC |