March 3, 2022

CBSE has introduced a new optional in their curriculum named Applied Maths. Linear programming is among the chapters included in the Applied maths syllabus.

Let us understand in deep about the topics involved in this chapter, important formulas, study materials or notes, and sample questions.

Linear Programming is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. It is a special case of mathematical programming (also known as mathematical optimization) and it is the calculation of best outcomes under given situations.

- The aim of the CBSE 12 Applied Maths Linear programming is to introduce you to the concept of Mathematical Modelling and build a strong foundation of concepts involved in it. Once you understand the basics of how Linear programming works, you will be able to calculate the best outcome of events under giver situations and maybe make better judgments in your life.
- The programs related to linear programming can be expressed in canonical form.
- Linear programming has proven useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design.
- In this post, you can get complete details about the syllabus of linear programming CBSE class 12, how to prepare for linear programming topic, etc.

You can read about **What is Applied Mathematics **to know about the subject in detail. It is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, business, computer science, and industry.

Watch Free Applied Mathematics Classes

Before you begin with the preparation, it is important to go through the complete **CBSE Class 12 Applied Maths Syllabus** so that you are aware of all important topics. Some of the topics covered in Linear programming are Constraints, Mathematical Formulation, and Feasible Regions and Graphs.

Let us have a look at CBSE Class 12 Linear programming syllabus in detail and you can plan your preparation accordingly.

- Introduction and related terminologies (constraints, objective function, optimization)
- The mathematical formulation of linear programming problems
- Different types of linear programming problems (Transportation and
- assignment problem)
- Graphical method of solution for problems in two variables
- Feasible and infeasible regions (bounded and unbounded)
- Feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints)

Read About **CBSE Class 12 Applied Maths Probability**

Linear Programming is an elemental part of Class 12 Applied mathematics Curriculum. It is one of the most important topics asked in the CBSE Class 12 Board Exams*. *

Moreover, the syllabus of CBSE Class 12 Linear programming comprises topics involving logics and algorithms so do not have to learn most of the stuff, once you understand the process and logic, you are good to go.

Thus you need to pay attention to the subject because CBSE Linear programming of Class 12 fetches you more marks at the same effort when compared to other topics of Applied Mathematics such as Numerical Applications and Calculus.

Subject |
Periods |
Weightage |

Linear Programming | 25 |
08/80 |

Read About **CBSE Class 12 Applied Maths Algebra**

From Linear programming, you can expect to inculcate mathematical language and symbolism. This is encouraged for you to communicate and relate to everyday experiences mathematically. So that you are able to understand the concepts and their utility in a much more profound way. In addition, the subject intends you to reinforce the logical reasoning skills.

- Some of the questions asked from the linear programming topic will be straightforward and will ask you directly to calculate, while some others will try to cloud the question with unnecessary data and information.
- And, some will even resemble questions from your textbook exercises and reference book examples.
- The purpose of questions in the CBSE Class 12 Linear programming exam is to test your adaptability to solve logic and form algorithms. You should not be afraid of dealing with complex situations in question. You should be agile and vigilant for any errors on the part of your calculation.
- You shall also be able to form algorithms and logic for calculating the best outcome with the help of linear programming. They will learn more about vectors, matrix, coefficients, planning, routing, scheduling, assignment, and design.

Read About **CBSE Class 12 Applied Maths Basic Financial with Mathematics**

In your journey towards acing any exam, Books/ Notes are your truest friend and mock papers are your biggest cheerleaders. Linear Programming Class 12 Notes are the crux of the entire topic.

They help you stay in your lane because subjects such as Linear programming have no boundary and no one ever knows when they move outside their syllabus and irrelevant information.

You can view or download the Linear Programming CBSE Class 12 Notes provided below and start their preparation accordingly.

Follow the list of CBSE Class 12 Linear Programming sample questions provided to you. Let them help you develop a complete idea and understanding of the topics involved before you begin studying it. As mentioned in the Linear programming Syllabus, topics under CBSE Class 12 Linear Programming vary from real-life problems to experimental situations. Let us look at some of the sample questions below.

We have provided a few CBSE Class 12 Linear Programming Problems to help you understand the type of question and knowledge that a Financial Mathematics Exam at Standard XI expects from you.

- Solve the following LPP graphically:
- Maximise Z = 2x + 3y, subject to x + y ≤ 4, x ≥ 0, y ≥ 0
- Solve the following linear programming problem graphically:
- Minimise Z = 200 x + 500 y subject to the constraints: x + 2y ≥ 10; 3x + 4y ≤ 24; x ≥ 0, y ≥ 0
- A manufacturing company makes two types of television sets; one is black and white and the other is color. The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a colored set. The company can spend not more than Rs 648000 a week to make television sets. If it makes a profit of Rs 510 per black and white set and Rs 675 per colored set, how many sets of each type should be produced so that the company has a maximum profit? Formulate this problem as an LPP given that the objective is to maximize the profit.
- A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food ‘I’ contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. Food ‘II’ contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs Rs 50 per kg to purchase Food ‘I’ and Rs 70 per kg to purchase Food ‘II’. Formulate this problem as a linear programming problem to minimize the cost of such a mixture.
- A man rides his motorcycle at a speed of 50 km/hour. He has to spend Rs 2 per km on petrol. If he rides it at a faster speed of 80 km/hour, the petrol cost increases to Rs 3 per km. He has almost Rs 120 to spend on petrol and one hour’s time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem.
- A company receives in sales $20 per book and $18 per calculator. The cost per unit to manufacture each book and calculator are $5 and $4 respectively. The monthly cost must not exceed $27,000 per month. If the manufacturing equipment used by the company takes 5 minutes to produce a book and 15 minutes to produce a calculator. How many books and calculators should the company make to maximize profit? Determine the maximum profit the company earns in a 30 day period?
- A self-employed carpenter $90 for the sale of a table and $180 for the sale of a rocking chair. It takes 2 hours for him to make a table and 5 hours to manufacture a rocking chair. He is limited to working 40 hours per week. The average manufacturing cost is $15 per table and $45 per rocking chair. He wishes to keep his manufacturing cost at $ 315 per week. How many tables and rocking chairs should he make to maximize his weekly sales? Determine the maximum sales and profit he can make per week.
- Some students want to start a business that cleans and polishes cars. It takes 1.5 hours of labor and costs $2.25 in supplies to clean a car. It takes 2 hours of labor and costs $1.50 in supplies to polish a car. The students can work a total of 120 hours a week. They also decide that they want to spend no more than $ 135 per week on supplies. The students expect to make a profit of $ 7.75 for each car that they clean and a profit of $ 8.50 for each car that they polish. What is the maximum profit the students can make?
- A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman’s time in its making while a cricket bat takes 3 hours of machine time and 1 hour of craftsman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time.

(i) What number of rackets and bats must be made if the factory is to work at full capacity?

(ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.

Read About **CBSE Class 12 Applied Maths Inferential Statistics**

Scoring more marks depends on how you prepare for the subject. How you Prepare for the subject depends on what your CBSE Class 12 Linear programming Preparation Strategy is.

We shall discuss the most important points that you should consider while preparing for CBSE Class 12 Linear programming. Some of the major guidelines for preparation include:

**Follow the Syllabus**: CBSE Class 12 Linear Programming Syllabus is of the utmost importance when it comes to the preparation of Linear programming. Ensure to prepare a proper study plan at your convenience and make sure to cover each topic.

**Use real-life/experimental examples: **Try to involve real-life examples of things happening around you and solve them using concepts you have learned in your subject. This will not only help you revise the topics but will also help brush up your skills. Practicing with original events helps clear doubts multi-fold and far quicker than general textbook study.

**Solve a Reference Book**: After you have completed your learning from NCERT you can refer to a reference book. Please note that** **this should be done after completing the NCERT Linear Programming Textbook and not before it.

**Practice Previous Year papers: **Linear programming NCERT Previous Year papers will help you with the exam pattern and trends of questions asked in the examination. Solving Linear programming Previous year papers will acquaint you with the Exam Pattern and the methods used to calculate the answer.

**Pen over Calculator**: Always prefer to solve sums on your own. The more you solve your problems manually, the better you understand them. It helps with your calculation skills and mental storage capacity which in turn helps you in solving even bigger and more complex questions later.

Read About **CBSE Class 12 Applied Maths Numerical Applications**

Frequently Asked Questions

CBSE Class 12 Linear Programming Scare Me, What should I do?

Acknowledge your negative thoughts regarding Linear Programming. Process them. Reason with them. You'll realise how unrealistic they are. Challenge the thoughts that say you are a failure and you can't succeed at Linear Programming. Remind yourself that it is just a subject that you can master.

CBSE Class 12 Linear Programming looks confusing, what if I fail?

So, you do badly. That’s it. But it is not the end of the world. People make mistakes, sometimes, even blunders, but that doesn’t make them less of people. Learn from your mistakes and use them as guiding light for your next exam.

How to attempt CBSE Class 12 Linear Programming Sample papers?

Set a timer. Keep all your stationery with you. Do not leave your desk until the timer stops. Answer each and every question as guided. Ask your folks not to disturb you while you are giving the exam. Do not exceed the timer. Do not cheat. Do not take help from books.

How to analyse Linear programming Sample paper Performance?

Consider yourself a teacher while studying your Linear programming Sample papers. Check each and every step. Never be lenient. If something is missing in the solution, or something is not as clear as it should be, penalise yourself for that. Calculate the total marks and reduce 10% against exam-related frenzy.

Additionally, Divide the Linear Programming topics asked into three lists of . Stronghold Linear programming Topics would be the ones you are best at and no question can steal marks away from you in these topics.

Territorial Topics of Linear programming would be a list of topics that you are good at but still has room for improvement. Alien topics would be the list of topics that are totally new to you and you never know how to begin in questions from these topics.

What if I don't get the marks in Linear programming I'm expecting?

It is okay. You know what your stronghold, territorial and alien subjects are. Make a realistic expectation of how you should be performing in the tests. And keep updating that list on the basis of your performance.

Updated On : March 3, 2022

CBSE has introduced a new optional in their curriculum named Applied Maths. Linear programming is among the chapters included in the Applied maths syllabus.

Let us understand in deep about the topics involved in this chapter, important formulas, study materials or notes, and sample questions.

Linear Programming is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. It is a special case of mathematical programming (also known as mathematical optimization) and it is the calculation of best outcomes under given situations.

- The aim of the CBSE 12 Applied Maths Linear programming is to introduce you to the concept of Mathematical Modelling and build a strong foundation of concepts involved in it. Once you understand the basics of how Linear programming works, you will be able to calculate the best outcome of events under giver situations and maybe make better judgments in your life.
- The programs related to linear programming can be expressed in canonical form.
- Linear programming has proven useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design.
- In this post, you can get complete details about the syllabus of linear programming CBSE class 12, how to prepare for linear programming topic, etc.

You can read about **What is Applied Mathematics **to know about the subject in detail. It is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, business, computer science, and industry.

Watch Free Applied Mathematics Classes

Before you begin with the preparation, it is important to go through the complete **CBSE Class 12 Applied Maths Syllabus** so that you are aware of all important topics. Some of the topics covered in Linear programming are Constraints, Mathematical Formulation, and Feasible Regions and Graphs.

Let us have a look at CBSE Class 12 Linear programming syllabus in detail and you can plan your preparation accordingly.

- Introduction and related terminologies (constraints, objective function, optimization)
- The mathematical formulation of linear programming problems
- Different types of linear programming problems (Transportation and
- assignment problem)
- Graphical method of solution for problems in two variables
- Feasible and infeasible regions (bounded and unbounded)
- Feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints)

Read About **CBSE Class 12 Applied Maths Probability**

Linear Programming is an elemental part of Class 12 Applied mathematics Curriculum. It is one of the most important topics asked in the CBSE Class 12 Board Exams*. *

Moreover, the syllabus of CBSE Class 12 Linear programming comprises topics involving logics and algorithms so do not have to learn most of the stuff, once you understand the process and logic, you are good to go.

Thus you need to pay attention to the subject because CBSE Linear programming of Class 12 fetches you more marks at the same effort when compared to other topics of Applied Mathematics such as Numerical Applications and Calculus.

Subject |
Periods |
Weightage |

Linear Programming | 25 |
08/80 |

Read About **CBSE Class 12 Applied Maths Algebra**

From Linear programming, you can expect to inculcate mathematical language and symbolism. This is encouraged for you to communicate and relate to everyday experiences mathematically. So that you are able to understand the concepts and their utility in a much more profound way. In addition, the subject intends you to reinforce the logical reasoning skills.

- Some of the questions asked from the linear programming topic will be straightforward and will ask you directly to calculate, while some others will try to cloud the question with unnecessary data and information.
- And, some will even resemble questions from your textbook exercises and reference book examples.
- The purpose of questions in the CBSE Class 12 Linear programming exam is to test your adaptability to solve logic and form algorithms. You should not be afraid of dealing with complex situations in question. You should be agile and vigilant for any errors on the part of your calculation.
- You shall also be able to form algorithms and logic for calculating the best outcome with the help of linear programming. They will learn more about vectors, matrix, coefficients, planning, routing, scheduling, assignment, and design.

Read About **CBSE Class 12 Applied Maths Basic Financial with Mathematics**

In your journey towards acing any exam, Books/ Notes are your truest friend and mock papers are your biggest cheerleaders. Linear Programming Class 12 Notes are the crux of the entire topic.

They help you stay in your lane because subjects such as Linear programming have no boundary and no one ever knows when they move outside their syllabus and irrelevant information.

You can view or download the Linear Programming CBSE Class 12 Notes provided below and start their preparation accordingly.

Follow the list of CBSE Class 12 Linear Programming sample questions provided to you. Let them help you develop a complete idea and understanding of the topics involved before you begin studying it. As mentioned in the Linear programming Syllabus, topics under CBSE Class 12 Linear Programming vary from real-life problems to experimental situations. Let us look at some of the sample questions below.

We have provided a few CBSE Class 12 Linear Programming Problems to help you understand the type of question and knowledge that a Financial Mathematics Exam at Standard XI expects from you.

- Solve the following LPP graphically:
- Maximise Z = 2x + 3y, subject to x + y ≤ 4, x ≥ 0, y ≥ 0
- Solve the following linear programming problem graphically:
- Minimise Z = 200 x + 500 y subject to the constraints: x + 2y ≥ 10; 3x + 4y ≤ 24; x ≥ 0, y ≥ 0
- A manufacturing company makes two types of television sets; one is black and white and the other is color. The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a colored set. The company can spend not more than Rs 648000 a week to make television sets. If it makes a profit of Rs 510 per black and white set and Rs 675 per colored set, how many sets of each type should be produced so that the company has a maximum profit? Formulate this problem as an LPP given that the objective is to maximize the profit.
- A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food ‘I’ contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. Food ‘II’ contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs Rs 50 per kg to purchase Food ‘I’ and Rs 70 per kg to purchase Food ‘II’. Formulate this problem as a linear programming problem to minimize the cost of such a mixture.
- A man rides his motorcycle at a speed of 50 km/hour. He has to spend Rs 2 per km on petrol. If he rides it at a faster speed of 80 km/hour, the petrol cost increases to Rs 3 per km. He has almost Rs 120 to spend on petrol and one hour’s time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem.
- A company receives in sales $20 per book and $18 per calculator. The cost per unit to manufacture each book and calculator are $5 and $4 respectively. The monthly cost must not exceed $27,000 per month. If the manufacturing equipment used by the company takes 5 minutes to produce a book and 15 minutes to produce a calculator. How many books and calculators should the company make to maximize profit? Determine the maximum profit the company earns in a 30 day period?
- A self-employed carpenter $90 for the sale of a table and $180 for the sale of a rocking chair. It takes 2 hours for him to make a table and 5 hours to manufacture a rocking chair. He is limited to working 40 hours per week. The average manufacturing cost is $15 per table and $45 per rocking chair. He wishes to keep his manufacturing cost at $ 315 per week. How many tables and rocking chairs should he make to maximize his weekly sales? Determine the maximum sales and profit he can make per week.
- Some students want to start a business that cleans and polishes cars. It takes 1.5 hours of labor and costs $2.25 in supplies to clean a car. It takes 2 hours of labor and costs $1.50 in supplies to polish a car. The students can work a total of 120 hours a week. They also decide that they want to spend no more than $ 135 per week on supplies. The students expect to make a profit of $ 7.75 for each car that they clean and a profit of $ 8.50 for each car that they polish. What is the maximum profit the students can make?
- A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman’s time in its making while a cricket bat takes 3 hours of machine time and 1 hour of craftsman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time.

(i) What number of rackets and bats must be made if the factory is to work at full capacity?

(ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.

Read About **CBSE Class 12 Applied Maths Inferential Statistics**

Scoring more marks depends on how you prepare for the subject. How you Prepare for the subject depends on what your CBSE Class 12 Linear programming Preparation Strategy is.

We shall discuss the most important points that you should consider while preparing for CBSE Class 12 Linear programming. Some of the major guidelines for preparation include:

**Follow the Syllabus**: CBSE Class 12 Linear Programming Syllabus is of the utmost importance when it comes to the preparation of Linear programming. Ensure to prepare a proper study plan at your convenience and make sure to cover each topic.

**Use real-life/experimental examples: **Try to involve real-life examples of things happening around you and solve them using concepts you have learned in your subject. This will not only help you revise the topics but will also help brush up your skills. Practicing with original events helps clear doubts multi-fold and far quicker than general textbook study.

**Solve a Reference Book**: After you have completed your learning from NCERT you can refer to a reference book. Please note that** **this should be done after completing the NCERT Linear Programming Textbook and not before it.

**Practice Previous Year papers: **Linear programming NCERT Previous Year papers will help you with the exam pattern and trends of questions asked in the examination. Solving Linear programming Previous year papers will acquaint you with the Exam Pattern and the methods used to calculate the answer.

**Pen over Calculator**: Always prefer to solve sums on your own. The more you solve your problems manually, the better you understand them. It helps with your calculation skills and mental storage capacity which in turn helps you in solving even bigger and more complex questions later.

Read About **CBSE Class 12 Applied Maths Numerical Applications**

Frequently Asked Questions

CBSE Class 12 Linear Programming Scare Me, What should I do?

Acknowledge your negative thoughts regarding Linear Programming. Process them. Reason with them. You'll realise how unrealistic they are. Challenge the thoughts that say you are a failure and you can't succeed at Linear Programming. Remind yourself that it is just a subject that you can master.

CBSE Class 12 Linear Programming looks confusing, what if I fail?

So, you do badly. That’s it. But it is not the end of the world. People make mistakes, sometimes, even blunders, but that doesn’t make them less of people. Learn from your mistakes and use them as guiding light for your next exam.

How to attempt CBSE Class 12 Linear Programming Sample papers?

Set a timer. Keep all your stationery with you. Do not leave your desk until the timer stops. Answer each and every question as guided. Ask your folks not to disturb you while you are giving the exam. Do not exceed the timer. Do not cheat. Do not take help from books.

How to analyse Linear programming Sample paper Performance?

Consider yourself a teacher while studying your Linear programming Sample papers. Check each and every step. Never be lenient. If something is missing in the solution, or something is not as clear as it should be, penalise yourself for that. Calculate the total marks and reduce 10% against exam-related frenzy.

Additionally, Divide the Linear Programming topics asked into three lists of . Stronghold Linear programming Topics would be the ones you are best at and no question can steal marks away from you in these topics.

Territorial Topics of Linear programming would be a list of topics that you are good at but still has room for improvement. Alien topics would be the list of topics that are totally new to you and you never know how to begin in questions from these topics.

What if I don't get the marks in Linear programming I'm expecting?

It is okay. You know what your stronghold, territorial and alien subjects are. Make a realistic expectation of how you should be performing in the tests. And keep updating that list on the basis of your performance.