Applications of Linear Programming in Optimization of Mechanical Engineering Systems

Linear Programming (LP) is one of the most powerful optimization techniques used in engineering for achieving optimal solutions under given constraints. In mechanical engineering, LP plays a crucial role in design optimization, production planning, resource allocation, scheduling, and energy management. This paper presents a comprehensive overview of the principles of linear programming and its practical applications in various mechanical engineering domains such as manufacturing, thermal systems, supply chain management, and maintenance planning. Mathematical formulation of LP problems, including objective functions and constraint equations, is discussed with illustrative examples. The advantages of LP in improving productivity, reducing operational cost, and enhancing system efficiency are highlighted. The study also reviews recent developments and computer-based solution methods used in industrial applications. The outcomes of this research demonstrate that linear programming is an effective decision-making tool for optimizing complex mechanical systems under limited resources.