In simplex method, to get the initial feasible solution. We often use Big-M method. My question is can we simply use elementary row transformation to get basis fesible solution instead introduce extra variables?
2026-03-24 23:40:58.1774395658
Why we need Big-M method in simplex method?
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In the primal simplex method, you want an initial basic feasible solution that is feasible with respect to both the equation constraints $Ax=b$ and to lower/upper bound constraints $l \le x \le u$. Conventional row operations can easily help you find a nonsingular subset of the columns of $A$ (a basis matrix, $B$), but this wouldn't help you in finding a basic solution that is feasible with respect to the bounds constraints $l \le x \le u$.