In linear programming, what defines a basic feasible solution?

• A. A feasible point where all variables are nonzero
• B. A feasible point where the objective value is maximized
• C. A feasible point where the number of positive variables equals the number of constraints, corresponding to a vertex
• D. A feasible point with all constraints satisfied with equality

Answer: (C)

The idea being tested is how a basic feasible solution (BFS) is formed in linear programming. A BFS corresponds to a corner point (vertex) of the feasible region, created when exactly as many independent constraints are binding as there are decision variables. In practice, you solve the system for a set of basic variables by turning the other variables to zero. If those basic variables come out nonnegative, you have a feasible BFS. When, in a nondegenerate case, all those basic variables are positive, their count equals the number of constraints, and the point sits at a vertex.

That matches the described concept: a feasible point where the number of nonzero variables equals the number of constraints, corresponding to a vertex. Note that BFS can still occur with some basic variables equal to zero in degenerate cases, and optimality is about the objective function value, not the BFS definition itself.