Feasibility

Definition

Feasibility refers to the condition of being possible or practical within a given context, especially concerning the constraints outlined by linear inequalities. In scenarios involving two-variable inequalities, feasibility indicates whether a certain set of values satisfies all the conditions imposed by those inequalities. This concept is crucial for determining valid solutions in optimization problems where certain criteria must be met.

5 Must Know Facts For Your Next Test

1. Feasibility is determined by checking if a proposed solution lies within the shaded region of the graph formed by the linear inequalities.
2. If there are no overlapping areas among the inequalities, it indicates that there are no feasible solutions for the system.
3. Feasible solutions can be bounded (limited area) or unbounded (infinite area), depending on the nature of the inequalities.
4. In linear programming, determining feasibility is the first step before finding an optimal solution.
5. Graphical methods can visually represent feasibility, making it easier to identify valid solution regions.

Review Questions

• How do you determine if a solution is feasible in a system of linear inequalities?
  • To determine if a solution is feasible in a system of linear inequalities, you check whether the proposed solution satisfies all the inequalities simultaneously. This involves substituting the values of the solution into each inequality and verifying if they hold true. If the solution meets all conditions, it lies within the feasible region; otherwise, it is considered infeasible.
• Discuss the implications of having an unbounded feasible region in linear programming.
  • An unbounded feasible region in linear programming means that there are infinitely many solutions that satisfy the constraints. This situation can arise when there are no restrictions on one or more variables, allowing them to take on arbitrarily large values. While this could lead to an infinite number of feasible solutions, it can complicate finding an optimal solution since the objective function may not have a maximum or minimum value within an unbounded area.
• Evaluate how understanding feasibility impacts decision-making in real-world scenarios involving linear programming.
  • Understanding feasibility is critical for effective decision-making in real-world scenarios because it helps identify viable options under specific constraints. By analyzing feasible regions, decision-makers can ensure that their strategies align with practical limits such as budget, resources, or time. Recognizing which solutions are feasible allows for better planning and execution, ultimately leading to more successful outcomes in fields like economics, logistics, and resource management.

Related terms

Solution Set: The collection of all possible solutions that satisfy a given system of inequalities.

Bounded Region: A closed and limited area on a graph where feasible solutions reside, typically formed by the intersection of linear inequalities.

Optimal Solution: The best possible solution from the feasible set that maximizes or minimizes an objective function in linear programming.