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Shadow Price Formula:
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Shadow Price represents the rate of change in the objective function value per unit increase in a constraint's right-hand side in linear programming. It indicates the marginal value of relaxing a constraint and is a key concept in sensitivity analysis.
The calculator uses the Shadow Price formula:
Where:
Explanation: The shadow price measures how much the optimal value of the objective function would improve if the constraint was relaxed by one unit.
Details: Shadow prices are crucial for understanding the sensitivity of optimal solutions to changes in constraints, helping decision-makers identify which constraints are binding and where resources should be allocated for maximum benefit.
Tips: Enter the change in objective value (in currency units) and the corresponding change in constraint (in units). The change in constraint must be non-zero for valid calculation.
Q1: What does a zero shadow price indicate?
A: A zero shadow price indicates that the constraint is not binding at the optimal solution, meaning relaxing the constraint won't improve the objective function.
Q2: Can shadow prices be negative?
A: Yes, shadow prices can be negative, indicating that increasing the constraint's right-hand side would actually worsen the objective function value.
Q3: How are shadow prices used in resource allocation?
A: Shadow prices help identify which resources are most valuable at the margin, guiding decisions about where to invest additional resources for maximum return.
Q4: Do shadow prices remain constant?
A: Shadow prices are valid only within the allowable range of constraint changes. Beyond certain limits, the basis of the optimal solution may change.
Q5: How do shadow prices relate to dual variables?
A: In linear programming, shadow prices are equivalent to the optimal values of the dual variables associated with the constraints.