Suppose we approach the solution of the usual linear program: subject to: x j = 0 (j = 1, 2, . . ….

 Suppose we approach the solution of the usual linear program:

Suppose we approach the solution of the usual linear program: subject to: x j = 0 (j = 1, 2, . . . ,...

subject to:

                                                                                             xj ≥ 0 (j = 1, 2, . . . , n).

 Show that the dual of (30) is given by:

                                                Minimize L(λ1, λ2, . . . , λm),

 subject to:

                                                      λi ≥ 0 (i = 1, 2, . . . , m).

 [Note: The Lagrangian function L(λ1, λ2, . . . , λm) may equal +∞ for certain choices of the Lagrange multipliers λ1, λ2, . . . , λm. Would these values for the Lagrange multipliers ever be selected when minimizing L(λ1, λ2, . . . , λm)?]

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