Linear Programming Foundations for High School Mathematics

Solving optimization problems is a fundamental skill in mathematics, economics, and data science, yet many students struggle to translate real-world constraints into solvable mathematical models. This written course simplifies the core concepts of linear programming, guiding you step-by-step from foundational definitions to graphical solutions. You will learn how to approach optimization problems systematically, building a strong analytical foundation that prepares you for high school exams and future quantitative studies. What you'll learn: Understand the core terminology of linear programming, including objective functions, constraints, and decision variables; Formulate mathematical models from real-world scenarios such as manufacturing, transport, and diet problems; Graph linear inequalities and identify the feasible region on a coordinate plane; Determine optimal solutions using the corner point method and evaluate bounded and unbounded regions; Recognize special cases in optimization, including multiple optimal solutions and infeasible problems. The course begins with essential definitions and theoretical foundations before guiding you through step-by-step graphical solution methods and practical problem-solving exercises. This course is designed specifically for high school mathematics students and beginners with a basic understanding of coordinate geometry and linear equations. Start building your mathematical optimization skills today.