Duality in Linear Programming 4

Duality in Linear Programming4In the preceding chapter on sensitivity analysis, we saw that the shadow-price interpretation of the optimalsimplex multipliers is a very useful concept. First, these shadow prices give us directly the marginal worthof an additional unit of any of the resources. Second, when an activity is priced out using these shadowprices, the opportunity cost of allocating resources to that activity relative to other activities is in Linear Programming is essentially a unifying theory that develops the relationships between agiven Linear program and another related Linear program stated in terms of variables with this shadow-priceinterpretation. The importance of Duality is twofold. First, fully understanding the shadow-price interpretationof the optimal simplex multipliers can prove very useful in understanding the implications of a particularlinear- Programming model.

simply net marginal revenues (i.e., marginal revenue minus marginal cost). For the basic variables x1 and x3, the reduced costs are zero, c1 =6 −11(1 2)− 1 2 (1) =0, c3 =13 −11(1)−1 2 (4) =0. The values imputed to the resources are such that the net marginal revenue is zero on those activities operated at a positive level.

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