Linear Programming: Formulate and Solve Optimization Problems

Optimization is at the heart of strategic decision-making, resource allocation, and mathematical analysis. Understanding how to model real-world constraints mathematically allows you to find the most efficient solutions to complex operational challenges. This text-only course guides you through the core principles of Linear Programming Problems (LPP), helping you progress from basic terminology to advanced solution methods. You will learn to formulate, analyze, and solve linear models both manually and using modern computational tools. By reading detailed mathematical explanations and practicing with structured written exercises, you will build a robust framework for solving optimization problems. What you'll learn: - Understand the fundamental terminology, core definitions, and mathematical structure of linear programming. - Formulate real-world scenarios into precise linear objective functions and constraint equations. - Solve two-variable problems using graphical analysis and identify feasible regions. - Master the Simplex method and duality theory for solving multi-variable optimization problems. - Apply modern computational solvers using Python libraries to automate complex linear programming calculations. - Analyze sensitivity and shadow prices to understand how changes in constraints affect the optimal solution. The course begins with foundational concepts, key definitions, and basic graphical representations before moving step-by-step into algebraic methods like Simplex and duality. You will then explore modern programmatic applications to bridge academic theory with practical engineering and business scenarios. This course is designed for beginners in optimization, mathematics students preparing for competitive exams, and data analysts looking to build a strong foundation in linear programming. No advanced mathematical background is required. Start reading today to master the science of optimal decision-making.