The global economic crisis forces many industrial companies to be more concerned in reducing unnecessary cost, and eliminating all possible wastes inside the production lines. So that, most of companies focused on adopting the lean production tools [1]. The core idea of lean manufacturing is actually quite simple; relentlessly work on eliminating wastes from the manufacturing process. These wastes have a direct impact on costs, and profit [2]. Real-life problems can be modelled as linear programs. Linear programming is a problem-solving approach developed for situations involving maximizing or minimizing a linear function subject to linear constraints that, limit the degree to which the objective can be pursued. The objectives of this paper are to develop methods to reduce the waste in the different manufacturing processes in a technical support unit of Airplanes. This paper focuses on developing a linear programming approach in order to reduce the waste of material used in the production line. Single Minute Exchange of Die methodology (SMED) was implemented in order to reduce the changeover time. The achieved results showed that the linear programming is an effective and cheapest tool in optimizing the waste in the production lines. By using linear programming, the organization can reduce the wasted materials from 15.1% to 6.6%, with annual costs saving 288,480 Egyptian pounds (EGP). The achieved results from implementing a simple lean production tool such as, SMED helps the organization to reduce the changeover time by 44%, with annual costs saving 29,440 EGP.