An infeasible problem has no solution that satisfies all constraints, while an unbounded problem has feasible solutions but the objective function can improve indefinitely without reaching a finite optimum.

By looking at the given problem, compare the constraints and check whether one constraint actually limits the feasible region or conflicts with another. If removing a constraint does not change the feasible region, it is redundant; if the constraints conflict and leave no feasible region, the problem is infeasible; if the objective can improve indefinitely, it is unbounded.

You can determine the differences by looking at the objective function, constraints, and decision variables. The objective shows whether the problem is maximizing or minimizing, while the constraints show the available limits or requirements. The decision variables tell you what decisions are being made and whether they are continuous or integer.

An infeasible special case occurs when a linear program has no solution that satisfies all constraints simultaneously, resulting in an empty feasible region caused by contradictory constraints. . In contrast, an unbounded special case occurs when a linear program has a valid, non-empty feasible region, but the objective function can be improved infinitely without violating any constraints because the feasible region extends infinitely in the direction of optimization.

You can identify the differences by looking for the main clue in the problem. Degeneracy occurs when a basic variable is equal to zero. Alternate optimal solution occurs when a nonbasic variable has zero reduced cost, meaning another optimal solution may exist. Unboundedness means the objective can continue improving without a limit. Infeasibility means there is no solution that satisfies all constraints. Redundancy means a constraint is unnecessary because it does not affect the feasible region.

To determine the difference between Infeasible and Unbounded special cases just by looking at a Linear Programming problem, compare the constraints and how they interact with the objective function

Infeasible problems feature contradictory constraints that leave no valid solution space, such as requiring a variable to be both greater than ten and less than five. Unbounded problems feature open-ended feasible regions lacking necessary limits, allowing the objective function value to grow infinitely.

You can determine the difference by looking at the constraints and the objective function. If the constraints limit the variables to a closed area, the feasible region is bounded; if the region can continue infinitely in at least one direction, it is unbounded. To know whether an optimal solution exists, look at the objective function: if it can keep increasing or decreasing as the feasible region extends infinitely, there is no finite optimal solution; if it reaches a highest or lowest value at a boundary point, then a finite optimal solution exists.