A single constraint can make an LP go from a unique optimum to infeasible if the new constraint removes the entire feasible region, including the previous optimal point. This happens when the changed constraint conflicts with other constraints, so no point can satisfy all constraints simultaneously. In the simplex method, this is detected when no feasible basic solution remains, such as a positive artificial variable remaining after Phase I.

A single constraint change causes an immediate jump to infeasibility when that constraint is actively binding at the optimal vertex and is shifted or rotated so that it contradicts another active constraint, destroying the shared intersection point and emptying the feasible region entirely.