This chapter commences with an introduction to linear programming. This is followed by a varied set of linear programming problems with their corresponding solutions. This chapter aims to help learn the formulation, resolution and interpretation of linear programming models and to show some of their applications in the industrial engineeringIndustrial engineering and management area. Hence new variants of basic product mix models and mixtures applied to Industrial Organisation Engineering and its management are proposed. Resolution methods are also reviewed: graphic methodLinear programminggraphic method and simplex methodLinear programmingsimplex method. Creating and solving dual problemsLinear programmingdual problems are also considered. Finally, special attention is paid to the economic interpretation of the results of some of the problems presented through their sensitive analysisLinear programmingsensitive analysis.