Can a linear programming problem become infeasible purely through the addition of a redundant constraint, or does infeasibility strictly require a system of mutually contradictory constraints?
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No, a linear programming problem cannot become infeasible through the addition of a truly redundant constraint. By definition, a redundant constraint is already implied by the existing system and is satisfied by every point in the current feasible region, meaning adding it leaves the solution space completely unchanged. Infeasibility strictly requires a system of mutually contradictory constraints that eliminates the feasible region entirely.
No, a linear programming problem cannot become infeasible purely by adding a redundant constraint because redundant constraints do not eliminate any valid points from the original feasible region; infeasibility strictly requires a system of mutually contradictory constraints whose intersection is empty.
A truly redundant constraint cannot make an LP infeasible because it does not eliminate any existing feasible solutions. Infeasibility occurs when the constraints conflict with each other so that no feasible point remains
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