What distinguishes an optimal solution from a basic feasible solution?

What distinguishes an optimal solution from a basic feasible solution?

• A. An optimal solution achieves the best objective value; a basic feasible solution is any feasible corner point
• B. A BFS is always optimal
• C. The optimal solution is always a BFS
• D. An optimal solution can be found without satisfying constraints

Answer: (A)

In linear programming, an optimal solution is the feasible point that gives the best value of the objective function (highest for maximize, lowest for minimize). A basic feasible solution is specifically a feasible corner point of the region—one vertex where enough constraints are binding to determine a solution. The key difference is that being feasible and being best are two separate ideas: a corner point (basic feasible) is a candidate, while the optimal solution is the candidate that actually yields the best objective value among all feasible points. If the objective is aligned with a constraint boundary, there can be multiple optimal solutions along an edge, with the endpoints of that edge being basic feasible solutions.

In linear programming, an optimal solution is the feasible point that gives the best value of the objective function (highest for maximize, lowest for minimize). A basic feasible solution is specifically a feasible corner point of the region—one vertex where enough constraints are binding to determine a solution. The key difference is that being feasible and being best are two separate ideas: a corner point (basic feasible) is a candidate, while the optimal solution is the candidate that actually yields the best objective value among all feasible points. If the objective is aligned with a constraint boundary, there can be multiple optimal solutions along an edge, with the endpoints of that edge being basic feasible solutions.