An improvement in the value of the objective function per unit increase in the right-hand side of a constraint is the

Question

BlackTom AI · Accepted Answer

Let’s break down the concepts involved in this question by examining what each term typically means in linear programming context.
Option 1: 'sensitivity value.' In LP literature, the term 'sensitivity analysis' refers to how changes in parameters affect the optimal solution, but there isn’t a standard metric specifically called 'sensitivity value' that measures the objective improvement per unit change in a constraint’s RHS. This phrasing is not the conventional terminology used for the effect of increasing RHS on the objective.
Option 2: 'constraint coefficient.' The constraint coefficient refers to the coefficients of decision variables within the constraint, not to any measure of how the objective changes when the RHS is altered. So this option describes a different element of the problem and does not capture the effect on the objective value.
Option 3: 'slack value.' Slack refers to the unused portion of a constraint at the optimal (or current) solution for ≤ constraints, or the excess for ≥ constraints. While related to the feasibility and tightness of a constraint, slack does not quantify how the objective improves per unit increase in the RHS; it measures remaining capacity, not the objective sensitivity.
Option 4: 'None of these are correct.' Since the standard term for the improvement in the objective per unit increase in a constraint’s RHS is known as the shadow price (or dual value) of the constraint, which is a classic concept in duality theory of linear programming, none of the listed terms precisely match that idea. The shadow price indicates how much the objective would improve (increase for minimization, decrease for maximization depending on sign conventions) per unit increase in the constraint's RHS, under the current basis.
To tie these thoughts together, recognize that the precise technical term is not among the first three options, so the most accurate choice among the given options points to the notion that the listed items do not capture the described sensitivity measure. The concept of a shadow price is the correct descriptor for this phenomenon, and it is not labeled in Options 1–3.

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