Question

Why do we consider the variable with negative coefficients in the pivot row to enter into the basis in dual simplex method?

Answer 1

Answer:

Recall that for the (usual) Simplex Method we can pick the entering variable to be any of the non-basic variables whose coefficient in the -row is positive (all of those choices serve to increase the objective function), but specific pivoting rules tell you exactly which one to pick: the standard rule says to pick one ...

Step-by-step explanation:

Answer 2

Answer:

• The Simplex Method1 pivots from feasible dictionary to feasible dictionary attempting to reach a dictionary whose -row has all of its coefficients non-positive. In sensitivity analysis certain modifications of an LP will lead to dictionaries whose -row “looks optimal” but that are not feasible. To take advantage of those those dictionaries, we will develop a dual version of the Simplex Method. Call a dictionary dual feasible if all the coefficients in its -row are non-positive. The Dual Simplex Method will pivot from dual feasible dictionary to dual feasible dictionary working towards feasibility.
• This new pivoting strategy is called the Dual Simplex Method because it really is the same as performing the usual Simplex Method on the dual linear problem. This also explains the term “dual feasible”: each dictionary for the primal has a corresponding dictionary for the dual and a primal dictionary is dual feasible exactly when the corresponding dictionary for the dual is feasible (in the usual sense). We won’t really take advantage of this correspondence, though: we won’t directly talk about the dual LP instead explaining how to perform these dual pivots directly on a dual feasible dictionary for the primal.