Linear Programming is an optimization technique where both the objective function and constraints are linear. The standard form is: maximize (or minimize) z = c₁x₁ + c₂x₂ + ... + cₙxₙ subject to linear constraints a₁₁x₁ + a₁₂x₂ + ... + a₁ₙxₙ ≤ b₁, and xᵢ ≥ 0. LP is used extensively in resource allocation, production planning, transportation, diet optimization, and financial portfolio management. The feasible region forms a convex polyhedron, and optimal solutions occur at vertices.