https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:linear-programming-ncert-new/x6f66cbee9a2f805b:linear-prgramming-problems-and-its-mathematical-formulation/v/introduction-to-linear-programming 2025-06-01T14:50:00.385158177Z Introduction to linear programming In this video, we introduce the fundamental concept of Linear Programming. We'll explore real-world scenarios where we need to find the best possible outcome given certain limitations, such as a sweet shop owner maximizing profit, a farmer maximizing income from their land, or a student maximizing their exam score. We'll break down what "Linear" and "Programming" mean in this context and discuss the wide-ranging applications of this powerful mathematical tool. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Introduction to linear programming In this video, we introduce the fundamental concept of Linear Programming. We'll explore real-world scenarios where we need to find the best possible outcome given certain limitations, such as a sweet shop owner maximizing profit, a farmer maximizing income from their land, or a student maximizing their exam score. We'll break down what "Linear" and "Programming" mean in this context and discuss the wide-ranging applications of this powerful mathematical tool. https://cdn.kastatic.org/ka-youtube-converted/hVI0oyhnuMw.mp4/hVI0oyhnuMw.mp4 208 Linear prgramming problems and its mathematical formulation https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:linear-programming-ncert-new/x6f66cbee9a2f805b:linear-prgramming-problems-and-its-mathematical-formulation/v/formulating-a-lpp 2025-06-01T14:50:00.385158177Z Formulating a LPP This video focuses on how to translate real-world optimization problems into the mathematical language of a Linear Programming Problem (LPP). We'll start with a furniture dealer problem, identifying the objective function (e.g., maximizing profit), decision variables (e.g., number of tables and chairs), and constraints (e.g., budget and storage). We'll then formulate a second example, a diet problem, which involves minimizing cost while meeting nutritional requirements. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Formulating a LPP This video focuses on how to translate real-world optimization problems into the mathematical language of a Linear Programming Problem (LPP). We'll start with a furniture dealer problem, identifying the objective function (e.g., maximizing profit), decision variables (e.g., number of tables and chairs), and constraints (e.g., budget and storage). We'll then formulate a second example, a diet problem, which involves minimizing cost while meeting nutritional requirements. https://cdn.kastatic.org/ka-youtube-converted/Lf_zgPcMIVE.mp4/Lf_zgPcMIVE.mp4 441 Linear prgramming problems and its mathematical formulation https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:linear-programming-ncert-new/x6f66cbee9a2f805b:linear-prgramming-problems-and-its-mathematical-formulation/v/solving-lpps-graphically 2025-06-01T14:50:00.385158177Z Solving LPPs graphically In this video, we begin to solve Linear Programming Problems using the graphical method. We'll learn how to plot the linear inequalities that represent the constraints of a problem on a graph. This process helps us identify the ""Feasible Region,"" which contains all possible solutions to the problem. We'll introduce the concept of corner points and explain why they are crucial for finding the optimal solution. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Solving LPPs graphically In this video, we begin to solve Linear Programming Problems using the graphical method. We'll learn how to plot the linear inequalities that represent the constraints of a problem on a graph. This process helps us identify the ""Feasible Region,"" which contains all possible solutions to the problem. We'll introduce the concept of corner points and explain why they are crucial for finding the optimal solution. https://cdn.kastatic.org/ka-youtube-converted/gTkWm4uBuYg.mp4/gTkWm4uBuYg.mp4 451 Linear prgramming problems and its mathematical formulation https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:linear-programming-ncert-new/x6f66cbee9a2f805b:linear-prgramming-problems-and-its-mathematical-formulation/e/finding-feasible-regions 2025-08-08T02:45:51.78671331Z Finding feasible regions Finding feasible regions Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:linear-programming-ncert-new/x6f66cbee9a2f805b:linear-prgramming-problems-and-its-mathematical-formulation/v/corner-point-method 2025-06-01T14:50:00.385158177Z Corner point method This video explains the Corner Point Method, a fundamental technique for solving Linear Programming Problems. We'll discuss the key theorem stating that the optimal solution (maximum or minimum) must occur at one of the corner points of the feasible region. We'll demonstrate the step-by-step process: find the coordinates of all corner points, substitute these points into the objective function, and compare the results to find the best possible outcome. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Corner point method This video explains the Corner Point Method, a fundamental technique for solving Linear Programming Problems. We'll discuss the key theorem stating that the optimal solution (maximum or minimum) must occur at one of the corner points of the feasible region. We'll demonstrate the step-by-step process: find the coordinates of all corner points, substitute these points into the objective function, and compare the results to find the best possible outcome. https://cdn.kastatic.org/ka-youtube-converted/cspdQ5OrfK4.mp4/cspdQ5OrfK4.mp4 406 Linear prgramming problems and its mathematical formulation https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:linear-programming-ncert-new/x6f66cbee9a2f805b:linear-prgramming-problems-and-its-mathematical-formulation/e/corner-point-method-for-optimisation 2025-08-08T02:45:51.78671331Z Corner point method for optimisation Corner point method for optimisation Ashish Gupta exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:linear-programming-ncert-new/x6f66cbee9a2f805b:linear-prgramming-problems-and-its-mathematical-formulation/v/special-cases-in-graphing-lpp 2025-06-01T14:50:00.385158177Z Special cases in graphing LPP In this video, we explore the special cases you might encounter when solving Linear Programming Problems. We'll discuss scenarios where there can be multiple optimal solutions, what happens when the feasible region is unbounded, and how to recognize when a problem has no feasible solution at all due to conflicting constraints. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Special cases in graphing LPP In this video, we explore the special cases you might encounter when solving Linear Programming Problems. We'll discuss scenarios where there can be multiple optimal solutions, what happens when the feasible region is unbounded, and how to recognize when a problem has no feasible solution at all due to conflicting constraints. https://cdn.kastatic.org/ka-youtube-converted/HxPNo348lAg.mp4/HxPNo348lAg.mp4 481 Linear prgramming problems and its mathematical formulation https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:linear-programming-ncert-new/x6f66cbee9a2f805b:linear-prgramming-problems-and-its-mathematical-formulation/e/special-cases-in-graphing-lpp 2025-08-08T02:45:51.78671331Z Special cases in graphing LPP Special cases in graphing LPP Ashish Gupta exercise