Basic solution (linear programming)  In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron formula_1 and a vector formula_2, formula_3 is a basic solution if:  A constraint is "active" for a particular solution formula_8 if it is satisfied at equality for that solution. A basic solution that satisfies all the constraints defining formula_1 or in other words, one that lies within formula_1 is called a basic feasible solution.