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Shadow Price Formula:
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The Shadow Price in Linear Programming represents the rate of change in the objective function value per unit increase in the right-hand side of a constraint, holding all other parameters constant. It indicates the marginal value of relaxing a constraint.
The calculator uses the Shadow Price formula:
Where:
Explanation: This ratio quantifies how much the objective function improves (or worsens) for each additional unit of resource availability or constraint relaxation.
Details: Shadow Prices are crucial in sensitivity analysis, helping decision-makers understand the value of resources, identify binding constraints, and optimize resource allocation in linear programming models.
Tips: Enter the change in objective function and change in constraint values. Both should be unitless quantities representing marginal changes. Ensure the constraint change is non-zero.
Q1: What does a positive shadow price indicate?
A: A positive shadow price indicates that relaxing the constraint would improve the objective function value.
Q2: Can shadow price be negative?
A: Yes, a negative shadow price means that increasing the constraint's right-hand side would decrease the objective function value.
Q3: What is the relationship between shadow price and dual variables?
A: In linear programming, shadow prices correspond to the optimal values of the dual variables associated with the constraints.
Q4: Are shadow prices constant?
A: Shadow prices remain constant within the range of the constraint's right-hand side where the current basis remains optimal.
Q5: How are shadow prices used in resource allocation?
A: Shadow prices help prioritize which resources to acquire or constraints to relax by showing which changes provide the greatest marginal benefit.