Special cases in Linear Programming include unboundedness- where the objective function can increase indefinitely without constraints; infeasibility-  where no solution satisfies all constraints; and degeneracy or alternate optimal solution - where multiple optimal solutions exist. These cases can impact industrial systems by indicating resource misallocation, unrealistic constraints, or inefficiencies, leading to challenges in achieving optimal production and planning.

Industrial systems are greatly impacted by specific circumstances in linear programming, such as unboundedness, infeasibility, and degeneracy. Unboundedness happens when the goal function can grow forever, which means there isn't an ideal solution. This is frequently the result of incorrect or absent restrictions. When no solution satisfies every constraint, this is known as infeasibility and can indicate that a model contains contradictory or unrealistic requirements, such as over specified production capacity. Degeneracy may result in wasteful resource allocation or cycling during solution processes when there are several optimal solutions or when certain constraints have no effect on the final result. In order to guarantee workable and feasible solutions for industrial processes, these unique instances may impede optimization attempts and necessitate modifications to system modeling or constraint definitions.