In linear programming, which option best defines a feasible solution?

• A. A solution that minimizes the objective function
• B. A solution that satisfies all constraints and nonnegativity
• C. A solution that violates at least one constraint
• D. A solution that ignores nonnegativity

Answer: (B)

In linear programming, feasibility means a proposed solution lies inside the bounds set by the model’s constraints. A feasible solution must satisfy every constraint and also respect nonnegativity if the model requires variables to be nonnegative. The collection of all such points forms the feasible region, the space where valid solutions live.

The best choice reflects this idea: it is a solution that satisfies all constraints and nonnegativity. That keeps it inside the feasible region, ready to be evaluated for optimality.

Options that involve minimizing the objective describe what we do after finding feasible solutions, not what makes a solution feasible. A solution that violates a constraint falls outside the feasible region and isn’t acceptable. Ignoring nonnegativity also breaks the model’s assumptions, making the solution infeasible.