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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?

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  • $\begingroup$ in algebraic formulation we add slack variable.I understood that much but then haven't we change the problem (i am still not convinced that it is the same)then we randomly choose to put any n-m number of variables to be zero.if the problem formualtion is same then only one variable should have changed not two(leaving basic and entering nonbasic).It seems like i have got into wrong understanding of simplex method.Please explain $\endgroup$ Mar 30, 2014 at 8:54

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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

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