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NCERT Solutions Class 12 Maths Chapter 12 Linear Programming
NCERT solutions for class 12 maths chapter 12 linear programming applies the systems of linear inequalities/equations to solve real-life problems. In earlier classes, kids have learned about the various systems of linear equations and how to solve day-to-day problems by utilizing them. Another topic introduced to students previously is linear inequalities and systems of linear inequalities in two variables as well as how to find their solutions by graphical methods. This lesson combines the knowledge of these two concepts with certain newer optimization topics. Optimization problems are a general class of questions that seek to maximize (or, minimize) profit (or, cost). Thus, an optimization problem may involve finding the maximum profit, minimum cost, or minimum use of resources, etc. NCERT solutions for class 12 maths chapter 12 elaborate on such sums with the help of linear programming.
Class 12 maths NCERT solutions chapter 12 is a simple but very important chapter with a wide range of industrial applications in finance, statistics, mathematics, economics, etc. There are many methods to solve linear programming problems however, this lesson focuses on the easiest technique, that is, the graphical approach. When kids are solving such questions the most important point they have to keep in mind is that after reading the problem sum the mathematical formulation should be done correctly. Once they are able to derive the correct equations, getting the final answer is very easy. The NCERT solutions Chapter 12 linear programming has a detailed explanation of all the NCERT textbook sums. In this article, we will explore the study tips and tricks that will ferry students to success in exams. , download the exercises provided in the links below.
- NCERT Solutions Class 12 Maths Chapter 12 Ex 12.1
- NCERT Solutions Class 12 Maths Chapter 12 Ex 12.2
- NCERT Solutions Class 12 Maths Chapter 12 Miscellaneous Ex
NCERT Solutions for Class 12 Maths Chapter 12 PDF
Linear programming problems came to the forefront in World War II when war operations had to be planned to minimize expenditure and maximize damage to the enemy. The first problem in linear programming was formulated in 1941 by the Russian mathematician, L. Kantorovich and the American economist, F. L. Hitchcock. However, both worked independently of each other. Further research gave birth to the concept as we know it today. There are many other such facts in the NCERT solutions class 12 maths that aim to provide a good understanding of linear programming while ensuring that kids remain motivated in studying these topics. The links to all these solutions are given below:
☛ Download Class 12 Maths NCERT Solutions Chapter 12 Linear Programming
NCERT Class 12 Maths Chapter 12
NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming
This chapter builds the foundation that is needed in performing linear regressions used for mathematical model analysis. Thus, kids need to develop a robust mathematical foundation of this subject matter. Additionally, the board exams usually have one or two long answer sums based on this topic. As it is extremely scoring children must make it a point to periodically revise the NCERT Solutions Class 12 Maths Chapter 12 linear programming so as to get full marks and not make any calculation mistakes. The exercise-wise in-depth analysis of each question is given below.
- Class 12 Maths Chapter 12 Ex 12.1 - 10 Questions
- Class 12 Maths Chapter 12 Ex 12.2 - 11 Questions
- Class 12 Maths Chapter 12 Miscellaneous Ex - 10 Questions
Topics Covered: The class 12 maths NCERT solutions chapter 12 is entirely based on linear programming. The topics covered are solving linear programming problems graphically, maximizing and minimizing a given equation as well as diet, manufacturing, and transportation questions.
Total Questions: Class 12 maths chapter 12 Linear Programming consists of 31 questions which can be further segregated into 14 simple, 10 tougher, and 7 complex high-order thinking sums.
List of Formulas in NCERT Solutions Class 12 Maths Chapter 12
NCERT solutions class 12 maths chapter 12 is not based on formulas rather it needs two other skills, namely, visualization and interpretation. Firstly, students need to interpret a problem sum and convert it into the correct minimization or maximization question. The next point is to draw the graph and shade the right area to represent the solution set. If children have issues in constructing the graph of a line, they can revisit topics on linear inequalities that they have seen in previous classes. Students must also learn how to pinpoint the optimal solution. The NCERT solutions for class 12 maths chapter 12 have certain terminologies that need to be understood before sums on the same can be solved. Some of them are as follows:
- Feasible or solution region: It is the common region determined by all the constraints including the non-negative constraints x ≥ 0, y ≥ 0 of a linear programming problem.
- Feasible solutions: These are the points within and on the boundary of the feasible region.
- Infeasible solution: These are the points outside the feasible region.
- Optimal solution: The point in the feasible region that gives the optimal value (maximum or minimum) of the objective function.
FAQs on NCERT Solutions for Class 12 Maths Chapter 12
Why are NCERT Solutions Class 12 Maths Chapter 12 Important?
NCERT Solutions Class 12 Maths Chapter 12 is essential for students preparing for boards and competitive exams. They give the step-by-step procedure to solving all the NCERT textbook sums as well as outline various tips and tricks that give a fast way of cross-checking the end result. Additionally, these solutions provide techniques to memorize formulas and concepts in a more efficient manner.
Do I Need to Practice all Questions Provided in NCERT Solutions Class 12 Maths Linear Programming?
The CBSE board exams follow the pattern set by the NCERT textbook. Also, the problems contained in this book have been designed to give kids a holistic knowledge of all the sections. Each sum targets a different aspect of the subject matter. Thus, students need to practice all the problems in the NCERT Solutions Class 12 Maths Linear Programming if they want to get fantastic results.
What are the Important Topics Covered in NCERT Solutions Class 12 Maths Chapter 12?
There are three types of questions in the NCERT Solutions Class 12 Maths Chapter 12 namely, transportation, dieting, and manufacturing problems. These form the crux of the lesson. Students are required to apply different graphical methods to solve these sums. They also study two fundamental theorems and the corner point technique to solve linear programming questions.
How Many Questions are there in NCERT Solutions Class 12 Maths Chapter 12 Linear Programming?
The NCERT Solutions Class 12 Maths Chapter 12 Linear Programming has 31 sums that are available in 3 exercises. These appear in different formats such as word problems and tabular questions. A student needs to frame the mathematical inequalities, find the solution and plot it on a graph. Most of the sums are fairly easy to understand however, the ones that appear in the miscellaneous exercise require higher-order thinking.
How CBSE Students can utilize NCERT Solutions Class 12 Maths Chapter 12 effectively?
Kids need to first go through the theory outlined in every section of the NCERT textbook. Then it is advisable to practice all the solved examples. While doing so in case students hit roadblocks they can revisit these concepts in previous chapters. Finally, the NCERT Solutions Class 12 Maths Chapter 12 can be used to cross-reference the answers and give clarity on the procedure that needs to be followed while solving similar problems.
Why Should I Practice NCERT Solutions Class 12 Maths Linear Programming Chapter 12?
If a student wants to gain mastery over a subject practice is the way to go. The 12th board can prove to be a difficult exam due to the uncertainty of the level of questions that can appear. Thus, to get the best possible score kids to need to practice each and every question of the NCERT Solutions Class 12 Maths Linear Programming Chapter 12 at least twice. In addition to this, they also need to go through the question papers of the past examinations so as to get a good understanding of the paper pattern.