Feasible solution

Definition

A feasible solution refers to a set of decision variables that satisfy all the constraints imposed by a linear programming model. It is essential in optimization as it represents the potential solutions that can be further evaluated to determine the best outcome. Feasible solutions must adhere to limitations such as resource availability, budget constraints, and operational requirements, allowing for practical implementation in real-world scenarios.

5 Must Know Facts For Your Next Test

1. Feasible solutions can be found graphically in two-variable problems by identifying where the constraints intersect.
2. Not all feasible solutions are optimal; an optimal solution is always within the feasible region but not all feasible solutions will provide the best outcome.
3. The feasible region is typically visualized as a polygon in two-dimensional space, bounded by the constraints.
4. A problem can have multiple feasible solutions or just one, depending on the nature of the constraints.
5. If no feasible solution exists, it indicates that the constraints are too restrictive or contradictory.

Review Questions

• How do you determine whether a solution is feasible within a linear programming model?
  • To determine if a solution is feasible, you check if it satisfies all of the constraints imposed by the model. This involves substituting the proposed values of the decision variables into each constraint and ensuring that they hold true. If all constraints are met, then the solution is considered feasible; if any constraint is violated, it is not feasible.
• Discuss how feasible solutions relate to both optimal solutions and constraints in a linear programming context.
  • Feasible solutions exist within the confines of constraints set by a linear programming model. Among these solutions, an optimal solution is identified as the one that best meets the objective function while still being feasible. Thus, while all optimal solutions must be feasible, not all feasible solutions are optimal. Understanding this relationship helps in narrowing down potential candidates for optimality among various feasible options.
• Evaluate the implications of having no feasible solution in a linear programming problem and how it affects decision-making.
  • When there is no feasible solution in a linear programming problem, it indicates that the constraints are either conflicting or overly restrictive, making it impossible to meet all conditions simultaneously. This situation can significantly impact decision-making as it may require revisiting and potentially relaxing certain constraints or reevaluating objectives. Understanding this absence of feasibility pushes decision-makers to consider alternative strategies or approaches to find workable solutions within acceptable parameters.

Related terms

Optimal Solution: The best possible feasible solution that maximizes or minimizes the objective function in a linear programming problem.

Constraints: Restrictions or limitations on the values of decision variables in a linear programming model, defining the feasible region.

Feasible Region:

The set of all possible feasible solutions that meet the defined constraints in a linear programming problem.