CMA Intermediate · Operations Management and Strategic Management · Optimum Allocation of Resources - LPP
By the complementary slackness property of duality, if a primal constraint has positive slack (unused resource) at the optimal solution, then the corresponding dual variable:
The corresponding dual variable is zero. When a resource has unused slack at the optimum, an additional unit would not improve the objective, so its shadow price is nil. This is the complementary slackness condition linking primal slack and dual variables.
- AIs positive and equal to the slack
- BIs zeroCorrect
- CIs negative
- DIs equal to the objective function value
Explanation
If a resource is not fully used, an extra unit adds nothing to the objective, so its shadow price is zero. It is not equal to the slack, and dual variables in a standard maximisation are non-negative.
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