--- title: Basic solution (linear programming) slug: basic-solution-linear-programming qid: snapshot: enwiki-001104062631 content_hash: license: CC BY-SA 4.0 source: https://en.wikipedia.org/w/index.php?oldid=1104062631 tags: [20476732, 23468805, 26709293] --- # Basic solution (linear programming) > [!note] Provenance > Snapshot `enwiki-001104062631` · content root `…` > Derived from · Licensed CC BY-SA 4.0 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 P and a vector \mathbf{x}^* \in \mathbb{R}^n , \mathbf{x}^* is a basic solution if: # All the equality constraints defining P are active at \mathbf{x}^* # Of all the constraints that are active at that vector, at least n of them must be linearly independent. Note that this also means that at least n constraints must be active at that vector. A constraint is active for a particular solution \mathbf{x} if it is satisfied at equality for that solution. A basic solution that satisfies all the constraints defining P (or, in other words, one that lies within P ) is called a basic feasible solution. 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 P and a vector \mathbf{x}^* \in \mathbb{R}^n , \mathbf{x}^* is a basic solution if: All the equality constraints defining P are active at \mathbf{x}^* Of all the constraints that are active at that vector, at least n of them must be linearly independent. Note that this also means that at least n constraints must be active at that vector. A constraint is active for a particular solution \mathbf{x} if it is satisfied at equality for that solution. A basic solution that satisfies all the constraints defining P (or, in other words, one that lies within P ) is called a basic feasible solution. ==References==