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# Linear Programming NCERT Solutions Class 12 Maths Chapter 12 Exercise 12.1 12.2 Miscellaneous Free pdf Notes Study Material download-Anand Classes

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming is designed and prepared by the expert teachers of ANAND CLASSES. All the important topics are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

Chapter 12 – Linear Programming covers multiple exercises. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. This will prove to be most helpful to you in your home assignments as well as practice sessions.

# Class 12 Maths NCERT Solutions Chapter 12 Linear programming

The Class 12 Maths NCERT Solutions of the chapter Linear Programming are prepared as per the latest CBSE syllabus and are very easy to understand, as the subject experts at ANAND CLASSES’S ensure that the solutions are given in the simplest form. These NCERT Solutions for Class 12 Maths Chapter 12 cover all the exercise questions included in the book and are in accordance with the latest CBSE Syllabus and its guidelines.

### 12.1 Introduction

This section recollects the discussion of linear equations, linear inequalities, and applications of linear inequalities in previous grades. It introduces the concept of optimisation problems and a special case of optimisation problem called linear programming problem, using an example. An ideal example of optimisation would be maximising the profit and minimising the cost of a production unit.

### 12.2 Linear Programming Problem and its Mathematical Formulation

This section consists of an example of a furniture dealer who is trying to maximise profits by choosing and experimenting with different combinations of buying chairs and tables.

12.2.1 Mathematical formulation of the problem

• This section further explains the formulation of the above-mentioned mathematical problem. It defines the non-negative constraints, objective function, and decision variables.
• The optimal value of a linear function can be defined as an objective function.
• A linear programming problem is finding the optimal value [maximum or minimum] of a linear function of variables, which are subjected to certain conditions and satisfying a set of linear constraints.
• The variables involved in the objective function are called decision variables.
• The constraints are the restrictions on the variables.

### 12.2.2 Graphical method of solving linear programming problems

• This section comprises the definition of the feasible region, feasible solution and infeasible solution, optimal solution, and bounded and unbounded region of feasible solution. It briefs about the Corner Point Method, which is used to solve linear programming problems with solved examples.
• The region obtained by the constraints [including non-negative constraints] can be termed as the feasible region.
• The points within the feasible region are called feasible solutions.
• The points outside the feasible region are called infeasible solutions.
• The point in the feasible region which gives the optimal value of the objective function is called an optimal solution.

### 12.3 Different Types of Linear Programming Problems

In this section, the different types of linear programming problems are discussed.

12.3.1 Manufacturing problems

• These problems can be seen in the manufacturing sector in order to optimise production by maximising profits. The profits can be a function of the number of workers, working hours, materials required, the value of the product in the market, the demand for the product, the supply of the product etc.

12.3.2 Diet problems

• Such problems involve the optimisation of the amount of intake of different types of foods, which are required by the body to obtain necessary nutrients. The agenda of a diet problem will be selecting those foods with the required nutrient at a lesser cost.

12.3.3 Transportation problems

• These problems involve the transportation of manufactured goods efficiently to different places, such that the transportation cost is minimum. For big companies, the analysis of transportation costs is very much important, as it caters to a wide area.

Students can utilise the NCERT Solutions for Class 12 Maths Chapter 12 for any quick reference to comprehend complex topics.

### Exercise-wise NCERT Solutions for Class 12 Maths  Chapter 12 Linear Programming

• Exercise 12.1 Solutions – 10 Questions
• Exercise 12.2 Solutions – 11 Questions
• Miscellaneous Exercise on Chapter 12 Solutions – 10 Questions

# Frequently Asked Questions (FAQs) on NCERT Solutions for Class 12 Maths Chapter 12

Q1

### How many problems are there in each exercise of the NCERT Solutions for Class 12 Maths Chapter 12?

Chapter 12 of the NCERT Solutions for Class 12 Maths has three exercises.
• Exercise 12.1 Solutions – 10 Questions
• Exercise 12.2 Solutions – 11 Questions
• Miscellaneous Exercise on Chapter 12 Solutions – 10 Questions
Each and every problem is solved with utmost care to provide the students with accurate solutions, as per the CBSE guidelines.
Q2

### What do you mean by linear programming in Chapter 12 of NCERT Solutions for Class 12 Maths?

Linear programming is a concept in which the mathematical functions are subjected to constraints and are minimised or maximised accordingly. The objective functions and the constraints covered in this chapter are completely linear. For further deductions, the minimum and maximum values of the linear functions are plotted on the xy coordinate. The main objective of linear programming is to optimise the mathematical functions exposed to linear constraints.
Q3

### Where can I get NCERT Solutions for Class 12 Maths Chapter 12 online?

You can download the NCERT Solutions for Class 12 Maths Chapter 12 on ANAND CLASSES’S website. The solutions to all the problems are curated by the subject experts to provide the students with the best reference material to rely on. You can download both chapter-wise or exercise-wise solutions and get a clear idea about the problem-solving techniques that are implemented while answering the textbook problems.

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