Linear programming problems are a central subjects of several economic and financial models. This chapter is concerned with basic properties of linear programming problems and of their “dual” problems. The questions concerning algorithms, numerical methods, etc., such as the famous “simplex method”, due to G. B. Dantzig, are not treated and for these topics we refer the readers to the books quoted in the References. Here the basic notions of primal and dual problems are introduced, together with the fundamental optimality criteria for a linear programming problems. Section 5.4 treats the basic duality theorems, whereas Sect. 5.5 is concerned with further remarks, such as, sensitivity analysis for a linear programming problem.