W11_L1: Linear programming

Welcome to Week 11 Lecture 1 of the course "Programming, Data Structures and Algorithms using Python" by Prof. Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pages/BSCS2002.html Video Overview This lecture explores Linear Programming (LP) through a practical and intuitive production planning scenario. We begin by introducing the key components of LP — constraints, objective functions, and the concept of LP duality. The Simplex algorithm is explained as a greedy search technique that navigates the convex feasible region to find an optimal solution. Using the example of a hand-woven carpet company, we model a real-world optimization problem involving hiring, firing, overtime, and storage costs to meet changing monthly demand. The lecture concludes by addressing the challenge of integer constraints, explaining why Integer Linear Programming (ILP) is significantly more complex despite its practical importance. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a foundation certificate from IITM CODE (Centre for Outreach and Digital Education), diploma(s) from IIT Madras, or BSc/BS degrees from IIT Madras. For more details, Visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #LinearProgramming #Optimization #SimplexAlgorithm #LPDuality #ProductionPlanning #Constraints #ObjectiveFunction #FeasibleRegion #GreedyAlgorithm #IntegerProgramming #ConvexOptimization #OperationsResearch #MathematicalModeling #Manufacturing #SupplyChain #CostOptimization #IITMadras #PDSA #ComputerScience #AlgorithmDesign