Which of the following special cases does not require reformulation of the…

Answer: Alternate optimality does not require reformulation.

Why this is correct:

• Alternate optimality (multiple optimal solutions) means more than one basic feasible solution attains the same objective value. You can report any one of those optimal solutions; no reformulation of the model is required.

• You can detect alternate optima when a nonbasic variable has zero reduced cost at an optimal tableau. Moving along the optimal edge yields other optimal points.

• If you need to present all optimal solutions, parameterize the family of optima or express them as convex combinations of extreme points; this still does not require reformulating the original problem.

Why the other cases typically require reformulation:

• Infeasibility: There is no solution that satisfies all constraints. To obtain a feasible solution you must change the model (for example relax or correct constraints) or use methods like adding artificial variables and running a Phase I procedure to find feasibility.

• Unboundedness: The objective can improve without bound under the current constraints, so no finite optimum exists. To get a finite solution you must reformulate the model, for example by adding missing constraints or bounds or reviewing the objective for modeling errors.

Summary: Alternate optimality allows selecting an optimal solution produced by the solver without reformulation. Infeasibility and unboundedness signal model issues that typically require changing constraints or the problem formulation to obtain a valid finite solution.