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Explore the fundamentals of linear programming in this lecture from MIT's Principles of Discrete Applied Mathematics course. Learn the definition and core concepts of linear programs through two practical examples: the diet problem and a bake sale optimization scenario. Discover how to formulate linear programming problems in both standard form and canonical form, understanding the mathematical structures that make these optimization techniques so powerful. Delve into the concept of duality in linear programming, examining how every linear program has an associated dual problem that provides valuable insights into the original optimization challenge. Master the theoretical foundations that underpin one of the most important tools in operations research and applied mathematics, setting the stage for understanding how linear programming solves real-world optimization problems across industries from logistics to finance.
