## NCERT Maths Chapter 12 Linear Programming Class 12 Solutions - FREE PDF Download

## FAQs on NCERT Solutions Class 12 Maths Chapter 12 Linear Programming

**1. How many sums are there in the NCERT Solutions for Class 12 Maths Chapter 12- Linear Programming?**

There are 3 exercises in the NCERT Class 12 Maths Chapter 12. In the first exercise, Ex.-12.1, there are 10 sums. In the second exercise, Ex.-12.2, there are 11 sums, and in the miscellaneous exercise, there are 10 sums. All the sums in this chapter are solved with stepwise explanations in the NCERT Solutions for Class 12 Maths Chapter 12- Linear Programming.

**2. What is meant by Linear Programming in mathematics?**

In linear programming, mathematical functions are subjected to various constraints and thereby maximised or minimised accordingly. All the constraints and the objective functions dealt with in this chapter are linear. The maximum and minimum values of the linear functions are plotted on the xy coordinate for further deductions. The main purpose of linear programming is to optimise various mathematical functions in terms of linear constraints.

**3. Can I get NCERT Solutions for Class 12 Maths Chapter 12- Linear Programming online?**

Yes, you can get the NCERT Solutions for Class 12 Maths Chapter 12- Linear Programming on Vedantu. The solutions to all the sums are prepared by our subject matter experts for the reference of students. You can download and refer to the NCERT solutions to get a clear understanding of the best problem-solving techniques for the sums of linear programming. The stepwise solutions facilitate a self-study session as you can compare your answers with these expert solutions.

**4. Can I download the NCERT Solutions for Class 12 Maths Chapter 12- Linear Programming for free?**

Yes, you can download the NCERT Solutions for Class 12 Maths Chapter 12- Linear Programming for free from Vedantu. These NCERT Solutions are available in a PDF format and you can download the same from our mobile application as well. This feature of free downloadable NCERT Solutions of Vedantu enables all students with an internet connection to refer to the best study materials online.

**5. What are the fundamental theorems for linear programming?**

**Theorem 1**

Let us consider R as the feasible region for linear programming and let's consider z to be ax+by, which is the objective function. When z reaches an optimal value, whether it be maximum or minimum and the variables x and y are the subjects to constraints. This optimal value that occurs must occur at a corner point of the said feasible region.

**Theorem 2**

Let us consider R as the feasible region for the given linear programming problem and let z be ax+by, which is the objective function. When the R is bounded then z attains both the maximum and the minimum value of R where each recurs at the joint corner of JR.

**6. What are the steps followed to apply the corner point method?**

The steps used in applying the corner point method are as follows:

First, it is important to find the feasible regions in the given linear programming problem, and along with it determine the corner point. This can be done by inspection or by solving the two equations of the line that intersect at that point.

The next step evolves the evaluation of the objective function, ie, z= ax+by at each of the corner points. Denote M and m respectively as the largest and smallest values of the given points.

When the feasible regions are bounded, then M and m respectively attain the maximum and the minimum of the objective function at the corner points.

**7. What is a feasible region?**

A feasible region attributed to the common region is determined by all the constraints which include even the non-negative constraints x,y>0 of linear programming. All other regions that do not fall under the feasible regions are termed as the non-feasible regions.

**8. What is an objective function and a constraint?**

An objective function refers to the linear function, for instance, z=px+py, where p and q are the constants. This linear equation that needs to be maximised or minimised is referred to as the objective function. When restrictions or linear inequalities are placed on a variable in the linear programming problem it is known as constraints. It is important for the student to familiarise and be thorough with these concepts in order to be able to do well in the examination.

**9. How to prepare for Class 12 Maths Chapter 12?**

A subject such as Math demands a high amount of practice to be thorough with the concepts. With adequate and regular practice, the student will have all the important points at the tip of their fingers. Therefore, without any doubt, the student needs to practise all the exercises that this chapter entails. To add the icing to the cake, the students can turn towards the NCERT Solutions for Class 12 Maths Chapter 12 available on the Vedantu website and on the Vedantu app at free of cost. These solutions will prove to be the best source of guidance for the students making them exam ready.

10. What are the key components of a Linear Programming Problem (LPP) explained in Linear Programming Class 12 NCERT Solutions?

The key components of an LPP include:

Objective Function: A linear function that needs to be maximized or minimized.

Constraints: A set of linear inequalities or equations that define the feasible region.

Feasible Region: The region in the graph that satisfies all constraints.

Decision Variables: The variables that impact the objective function and are subject to the constraints.

11. What is Linear Programming in Linear Programming Class 12 Solutions PDF?

Linear Programming (LP) in Linear Programming Class 12 Solutions PDF is a method to achieve the best outcome in a mathematical model with linear relationships. It involves optimizing a linear objective function, subject to linear equality and inequality constraints.

12 What is the graphical method of solving Linear Programming Problems in Chapter 12 Maths Class 12?

The graphical method involves:

Plotting each constraint on a graph.

Identifying the feasible region where all constraints overlap.

Finding the corner points (vertices) of the feasible region.

Evaluating the objective function at each corner point to find the optimal solution.

13. How do you formulate a Problem in linear programming class 12 solutions?

Formulating an LPP in Class 12 linear programming involves:

Defining the decision variables.

Writing down the objective function.

Stating the constraints.

Ensuring all functions and constraints are linear.