Based on the per-unit increase in the right-hand side of the constraint, the shadow price measures the

Question

BlackTom AI · Accepted Answer

The question asks about the shadow price in the context of a linear programming constraint.
Option 1: 'change in the value of the objective function value.' This aligns with the standard interpretation of the shadow price: it measures how much the objective function would improve (or worsen) per additional unit of the constraint's right-hand side. In other words, it is the rate of change of the objective value with respect to a unit increase in RHS, so this option correctly describes the shadow price.
Option 2: 'change in the right hand side of a constraint.' This describes a change in the constraint itself (the RHS), not the impact on the objective function. The shadow price quantifies the effect on the objective given that RHS change, not the RHS change itself.
Option 3: 'change in the value of the optimal solution value.' While the objective value changes when the RHS changes, the wording here is circular and vague. The shadow price specifically relates the change in objective value to a unit change in RHS, not simply stating 'change in the optimal value' without tying it to the RHS increment.
Option 4: 'change in the objective function coefficient.' Changes in objective function coefficients are associated with different concepts (such as reduced costs or sensitivity to coefficients), not with the shadow price, which concerns the RHS of a constraint rather than the objective coefficients.

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