The four special cases in linear programming are unbounded solutions (infinite objective function values), infeasible solutions (no feasible variable sets), multiple optimal solutions (several variable combinations yielding the same optimal value), and degenerate solutions (basic variables equal to zero). Recognizing these cases is essential for effective problem-solving in LP.

The four special cases in linear programming are infeasibility, unboundedness, alternate optimal solutions, and redundant constraints. Infeasibility occurs when no feasible solutions meet all constraints, while unboundedness happens when the objective function can increase or decrease indefinitely. Alternate optimal solutions are multiple feasible solutions yielding the same optimal value, and redundant constraints are those that do not affect the feasible region or optimal solution and can be removed without changing the outcome.