Types Of Linear Programming Solutions:
LP problem solution falls in one of the following cases:
1. Feasible solution: Feasible solution is a solution which satisfies all the constraints and the non negativity restrictions.
2. Optimal solution: Problem is feasible and bounded: then there exists an optimal point; an optimal point is on the boundary of the feasible region.
There is always at least one optimal corner point (if the feasible region has a corner point).
If any non basic variable has not zero in the last row (Cj-Zj). There is unique solutions for the linear programming problem.
If the non basic variable has zero in the last row (Cj-Zj), there may have multiples solution for the linear programming problem.
3. Infeasible solution: A linear Problem is infeasible: Feasible region is empty i.e there exists no solution that satisfies all of the constraints at a time.
If all constraints are of ≤ type , then infeasible solution condition will not arise.
If any constraint is ≥ or = type, then we are using artificial variables.
If artificial variable will remain in basic variable even though the optimum solution has been reached, then such condition is known as infeasible solution.
4. Unbounded solution: Problem is unbounded: Feasible region is unbounded towards the optimizing direction. It is a situation where objective function is infinite without violating any of the constraints in the problem.
If the ratio of RHS/Pivot column become negative, thus it is not possible to determine the basic variable that should leave. Hence the LPP has unbounded solutions.
