Shadow price in Linear Programming

Shadow price in linear programming refers to the value assigned to one unit of a particular resource or constraint. It is the change in the objective function value per unit increase in the availability of a resource or constraint.

Significance of Shadow Price

The shadow price provides valuable information about the problem and helps in decision-making. It indicates the opportunity cost of using a resource or constraint. It helps in determining the economic feasibility of the problem and identifying the critical resources.

Calculation of Shadow Price

The shadow price can be calculated using the dual simplex method or sensitivity analysis. In the dual simplex method, the shadow price is the negative of the reduced cost of the corresponding dual variable. In sensitivity analysis, the shadow price is the change in the objective function value due to a unit increase in the availability of a resource or constraint.

Interpretation of Shadow Price

A positive shadow price indicates that an increase in the availability of a resource or constraint will increase the objective function value. A negative shadow price indicates that a decrease in the availability of a resource or constraint will increase the objective function value. A zero shadow price indicates that the resource or constraint is not binding.

Conclusion

In conclusion, the shadow price in linear programming refers to the value assigned to one unit of a particular resource or constraint. It provides valuable information about the problem and helps in decision-making. The shadow price can be calculated using the dual simplex method or sensitivity analysis.