Consider a linear program with bounded variables: where the upper bounds u j are positive…
Consider a linear program with bounded variables:
where the upper bounds u j are positive constants. Let yi for i = 1, 2, . . . , m and wj for j = 1, 2, . . . , m be variables in the dual problem.
a) Formulate the dual to this bounded-variable problem.
b) State the optimality conditions (that is, primal feasibility, dual feasibility, and complementary slackness) for the problem.
c) denote the reduced costs for variable x j determined by pricing out the ai j constraints and not the upper-bounding constraints. Show that the optimality conditions are equivalent to the bounded-variable optimality conditions.
given in Section 2.6 of the text, for any feasible solution x j (j = 1, 2, . . . , n) of the primal problem.