1. The problem is to understand what "basic feasible" means in the context of linear programming. 2. In linear programming, a "feasible solution" is any solution that satisfies all the constraints of the problem. 3. A "basic feasible solution" is a feasible solution that is at a vertex (corner point) of the feasible region. 4. Mathematically, if you have $m$ constraints and $n$ variables, a basic feasible solution is found by setting $n - m$ variables to zero and solving the remaining system of $m$ equations. 5. This solution must satisfy all constraints (including non-negativity) to be considered feasible. 6. Basic feasible solutions are important because the optimal solution to a linear programming problem, if it exists, lies at one of these points. Final answer: A basic feasible solution is a vertex of the feasible region obtained by setting $n - m$ variables to zero and solving the system, satisfying all constraints.