Linear Programming Algorithms: Foundations and Applications

Finding the most efficient way to allocate resources, minimize costs, or maximize profits is a fundamental challenge in business, engineering, and data science. Linear programming provides the mathematical framework to solve these optimization problems systematically. This text-based course guides you from the absolute basics of linear programming to understanding the core algorithms that power modern solvers. You will learn how to formulate real-world problems mathematically and translate them into code using modern Python optimization libraries. What you will learn: 1. Understand the core terminology of optimization, including decision variables, constraints, and objective functions. 2. Formulate real-world scenarios into structured linear programming models. 3. Explore the mechanics of classic optimization algorithms like the Simplex method and duality theory. 4. Apply modern Python libraries such as SciPy and PuLP to solve optimization models programmatically. 5. Analyze sensitivity and shadow prices to understand how changes in data affect optimal solutions. 6. Implement best practices for debugging infeasible or unbounded models in practical applications. The course begins with foundational concepts and geometric interpretations before progressing to algebraic algorithms and hands-on programmatic implementation. You will read detailed explanations, analyze step-by-step mathematical formulations, and practice with written exercises. This course is designed for beginners in operations research, data science, or computer science, with no prior optimization experience required. Start reading today to unlock the power of mathematical optimization and algorithmic problem-solving.