NCERT Solutions Class 12 Maths Chapter 12 Linear Programming is one of the most significant topics in the Class 12 Maths curriculum. Linear Programming is the process of optimizing a linear objective function, subject to a set of linear constraints. It is used in various fields such as business, economics, engineering, and more. In this blog, we will provide a comprehensive guide to NCERT Solutions Class 12 Maths Chapter 12 Linear Programming.
NCERT Solutions Class 12 Maths Chapter 12 Linear Programming is divided into two parts, namely:
Introduction to Linear Programming: This section covers the basics of linear programming, including the definition of linear programming, the standard form of linear programming problems, and the graphical method to solve linear programming problems.
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Linear Programming Problem and its Mathematical Formulation: This section explains how to formulate a linear programming problem mathematically. It covers topics such as linear programming problem and its mathematical formulation, the graphical method to solve linear programming problems, the simplex method to solve linear programming problems, and duality in linear programming.
Some of the essential topics covered in NCERT Solutions Class 12 Maths Chapter 12 Linear Programming are:
Linear Programming Problem and Its Mathematical Formulation:
Linear programming problem involves finding the maximum or minimum value of a linear objective function, subject to a set of linear constraints. It can be formulated mathematically using a set of linear inequalities or equations. The objective function and constraints are expressed in terms of decision variables, which are the unknowns in the problem. The goal is to optimize the objective function subject to the constraints.
Graphical Method to Solve Linear Programming Problems:
The graphical method is a graphical representation of linear programming problems. It involves plotting the constraints on a two-dimensional graph and identifying the feasible region. The optimal solution can be found by identifying the corner points of the feasible region and evaluating the objective function at each of these points.
Simplex Method to Solve Linear Programming Problems:
The simplex method is an algebraic method used to solve linear programming problems. It involves a systematic process of moving from one corner point of the feasible region to another until the optimal solution is found. The method involves the use of a tableau, which is a matrix representation of the problem.
Duality in Linear Programming:
Duality in linear programming refers to the relationship between the primal problem (original problem) and the dual problem (a related problem). The dual problem involves finding the minimum or maximum value of a linear function subject to a set of linear constraints. The duality theorem states that the optimal solution to the primal problem is equal to the optimal solution to the dual problem.
Sensitivity analysis is the process of analyzing the effect of changes in the parameters of a linear programming problem on the optimal solution. The analysis involves changing the values of the coefficients in the objective function or the constraints and observing the effect on the optimal solution. The sensitivity analysis helps in identifying the robustness of the solution and provides insight into the impact of changes in the parameters.
Transportation and Assignment Problems:
Transportation and assignment problems are special types of linear programming problems. The transportation problem involves finding the minimum cost of transporting a given quantity of goods from several sources to several destinations. The assignment problem involves assigning a set of tasks to a set of workers, subject to certain constraints, such as availability and expertise. Both problems can be solved using linear programming techniques.
To score well with NCERT Solutions Class 12 Maths Chapter 12 Linear Programming, students should follow these tips:
NCERT Solutions Class 12 Maths Chapter 12 Linear Programming is an essential topic that every student should understand thoroughly. Students can follow the tips mentioned above to score well in their exams. Also, Oswaal Books' NCERT Solutions Class 12 Maths Chapter 12 Linear Programming can be a valuable resource for students. By following this guide, students can easily master linear programming and excel in their exams.