Transcription of Duality in Linear Programming 4
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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.
Problem (2) is called the dual of Problem (1). Since Problem (2) has a name, it is helpful to have a generic name for the original linear program. Problem (1) has come to be called the primal. In solving any linear program by the simplex method, we also determine the shadow prices associated with the constraints.
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