What does the shadow price in an LP indicate?

What does the shadow price in an LP indicate?

• A. The current value of a slack variable
• B. The total cost of resources used
• C. The change in the objective per unit increase in any variable
• D. The amount the objective would improve per unit increase in a constraint's RHS, holding other factors constant

Answer: (D)

Shadow price, or the dual value, is the marginal value of relaxing a constraint. It tells you how much the objective function would improve if you increase the right-hand side of that constraint by one unit, holding all other data the same and keeping the current solution basis unchanged. If the constraint is binding at the optimum, this value shows the potential gain from having more of that resource (positive for a maximization problem, negative for a minimization problem). If the constraint isn’t tight, the shadow price is zero, meaning extra resource wouldn’t help the current solution. Keep in mind this sensitivity information is valid only within a certain range of RHS changes, beyond which the optimal basis may change and the shadow price can shift. In short, it’s the improvement in the objective per additional unit of that constraint’s resource.

Shadow price, or the dual value, is the marginal value of relaxing a constraint. It tells you how much the objective function would improve if you increase the right-hand side of that constraint by one unit, holding all other data the same and keeping the current solution basis unchanged. If the constraint is binding at the optimum, this value shows the potential gain from having more of that resource (positive for a maximization problem, negative for a minimization problem). If the constraint isn’t tight, the shadow price is zero, meaning extra resource wouldn’t help the current solution. Keep in mind this sensitivity information is valid only within a certain range of RHS changes, beyond which the optimal basis may change and the shadow price can shift. In short, it’s the improvement in the objective per additional unit of that constraint’s resource.