I am unable to understand algebraic formulation of Simplex method. When we add slack variables, and solve for finding basic feasible solution, we put free variables equal to zero. My question is: why zero? Being free variables, they could have been anything. How does that help in the Simplex algorithm?
2026-03-25 18:45:02.1774464302
Understanding why non-basic variables are set to zero in the Simplex Method
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The free variables are set to zero, so that the slack variables can be set to the right hand side coefficients, in a trivial manner.
Graphically speaking, with free variables other than zero, we are in the inside of the convex polyhedron.
Also, with free variables not set to zero, the solution depends on the complete coefficient matrix and not only the basis. And we cannot invert the complete coefficient matrix.
Inequality constraints and slack variables: Simplex alogrithm