In linear programming (LP), what do we call a constraint that does not change or restrict the feasible region at all?

Introduction / Context:
In linear programming models, constraints define the feasible region within which the objective is optimized. Sometimes a written constraint does not actually ‘‘bind’’ or change the region. Recognizing such constraints simplifies models and computation.

Given Data / Assumptions:

• An LP model with an objective and linear constraints.
• Graphical or algebraic feasibility analysis applies.
• We are identifying the correct term for a nonrestrictive constraint.

Concept / Approach:
A redundant constraint is logically implied by other constraints and the variable bounds. Removing it leaves the feasible region unchanged. It does not create a binding boundary at the optimum and has no effect on the solution set.

Step-by-Step Solution:

Verification / Alternative check:
Run the LP with and without the candidate constraint; identical feasible sets or identical optimal bases indicate redundancy.

Why Other Options Are Wrong:

• Slack variable: an artificial variable measuring unused capacity; not a constraint type.
• Unbounded solution: describes objective behavior, not a specific constraint.
• Surplus variable: measures excess over a ‘‘≥’’ constraint; again, not a constraint type.

Common Pitfalls:
Confusing redundant constraints with nonbinding constraints; a nonbinding constraint may still shape the feasible set even if it is not tight at the optimum.

Final Answer:
redundant constraint