Linear programming optimizes linear objective function subject to linear constraints. Graphical method: plot constraints, find feasible region (polytope), evaluate objective at corner points. Key concepts: constraints define inequalities, feasible region is intersection, optimal point at vertex. Shortcut: identify corner coordinates without detailed graphing. Simplex method: algebraic approach for multiple variables. Common traps: misidentifying feasible region, forgetting non-negativity constraints. Exam tips: always check constraint satisfaction. Time-saving: recognize maximization vs minimization from problem wording. Applications: resource allocation, production planning, cost minimization. Slack variables convert inequalities to equations. Pivot operations in simplex method. Standard form requirements: all constraints as ≤, all variables ≥ 0. Practice converting word problems to mathematical formulation. Corner point theorem: optimal value occurs at vertex of feasible region.