Linear programming is a mathematical optimization technique used to find the best possible solution to a problem with linear constraints. It involves maximizing or minimizing a linear objective function subject to linear constraints.
In Class 12 Mathematics syllabus, the topics of Linear Programming are covered in Chapter 7. The syllabus includes the following topics:
Introduction to Linear Programming: This includes the basic concepts and terminologies used in linear programming, such as objective function, decision variables, constraints, feasible region, and optimal solution.
Formulation of Linear Programming Problems: This includes the process of formulating a problem into a linear programming model, such as identifying the decision variables, formulating the objective function, and writing the constraints.
Graphical Method of Solution for Problems in Two Variables: This involves the graphical representation of the feasible region and the optimal solution in problems with two variables.
Simplex Method of Solution: This includes the algorithmic approach to solving linear programming problems with multiple variables, such as the simplex method and its variants.
Mathematical Formulation of Linear Programming Problems: This includes the mathematical notation and terminology used in linear programming, such as matrix notation, standard form, slack variables, and basis.
Applications of Linear Programming: Linear programming finds applications in various fields, including economics, finance, business, and engineering. The Class 12 Mathematics syllabus covers some of these applications, such as production planning, transportation, and assignment problems.
The study of linear programming provides a powerful tool for solving optimization problems and making optimal decisions in various real-world situations.