Linear programming is a most important optimization algorithm. It focuses on problems with linear objective function and linear constraints. The chapter describes the algorithm in detail, with examples and graphical representations. Some illustrative applications are also described, like optimal diets (yes, food), blending (gas and oil, paints, etc.), scheduling, special methods for logistics, transportation, job assignment, and network flows. The chapter includes several programs in MATLAB (for example, those based on linprog( ) function).