a shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint so long as the change is within the allowable increase.
What is a shadow price in linear programming?
Answer:
In linear programming, a shadow price represents the rate of change in the optimal value of the objective function per unit increase in the right-hand side of a constraint, assuming that the increase is within the allowable range. Shadow prices are essential in sensitivity analysis in linear programming as they provide information about how the optimal solution will change with changes in the constraints.
When the right-hand side of a constraint is increased by one unit, the shadow price indicates how much the optimal objective function value will increase. If the shadow price of a constraint is zero, it means that the constraint is not binding, and the optimal solution does not depend on that constraint. However, a positive shadow price implies that the constraint is binding, and if additional resources or relaxation are possible within the allowable increase, the objective function value will increase accordingly. On the other hand, a negative shadow price suggests that the constraint is not binding, and reducing the resources within the allowable decrease will not affect the optimal solution.
Shadow prices help decision-makers understand the incremental value of additional resources or constraints in optimization problems and are valuable indicators for managerial decision-making and resource allocation.