 When this process is complete the feasible region will be in the form

It is also useful to assume that the rank of formula_23 is the number of rows.This results in no loss of generality since otherwise either the system formula_24 has redundant equations which can be dropped, or the system is inconsistent and the linear program has no solution.A linear program in standard form can be represented as a "tableau" of the form 

The first row defines the objective function and the remaining rows specify the constraints.