With the onset of your higher secondary academic life, everything changes. Starting from your friend circle to the contents of your curriculum, everything. New and Exciting subjects like CBSE Class 12 Applied Mathematics, Economics, Poetry, Drama find their way to your school bag. And while you enjoy this totally new journey with subjects that are mostly new to you, it is highly recommended that you assess your preparation every now and then.

Today, in this article, we will be taking on CBSE Class 12 Linear Programming. It is a subset of newly introduced Applied Mathematics in CBSE Class 12 Curriculum. We will first understand what Applied Mathematics is. And then we will introduce you to Linear programming. We will also talk about the CBSE Linear Programming Syllabus, its weightage in your CBSE Class 12 Applied Maths Board Exam and what the subject expects from you.

We shall also discuss the preparation angle of the subject while at the same time, cover the most important preparation tips and how you should plan your CBSE Class 12 Linear programming Preparation strategy. Additionally, we will share important notes, guide you towards the leading books in the market, help you sort through practise questions and CBSE Class 12 Linear Programming Previous Year Papers. And finally, we will conclude this article by discussing and sharing most Frequently Asked Questions and queries of students regarding Applied Mathematics and CBSE Class 12 Linear Programming. Let us get right into it.

What is Applied Maths?

If you look around on Google and websites like Wikipedia, you’ll come to know that Applied Mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, business, computer science, and industry.

Let us break it down for you in simpler words. The subject, CBSE Class 12 Applied Mathematics is any math that is involved in fields other than math. Could we make you clear enough for you?

Let us try again by giving you an example. The math that you so frequently use in Physics to prove/ solve Newton’s Equations, well yes- that is Applied Mathematics. The Math that you often use in statistics to find out the mean, mode and median- well, Applied Mathematics. Calculations and sums that you do in Physical Chemistry-yes, you got it right- Applied Mathematics. The Math that is used to state governing equations of events in Experimental biology -well yes, Applied Mathematics. Similarly, Math that is used to predict the best outcome or chances of something happening-Yes. Again. Applied Mathematics and that is what constitutes CBSE Class 12 Linear Programming which will be studying in detail in this article.

The aim of CBSE 12 Applied Mathematics as per the notice shared by the board is to acknowledge the universal nature of mathematics. The curriculum wants you to appreciate CBSE Class 12 Applied Mathematics for its easy applications in diverse fields. Which when said out loud, interprets to- “We just want to show you that Math is involved in almost every field

What is CBSE Class 12 Applied Maths Linear programming?

So now that we know what Applied Mathematics is all about, it will be easier for us to understand Linear programming. In the previous section, while discussing Applied Mathematics, we dropped a hint on CBSE Class 12 Linear Programming. To explain it in the shortest choice of words, Linear programming is the calculation of the best outcome of any event.

As per Wikipedia, 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. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

CBSE 12 Applied Maths Linear programming 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. How cool is that!

CBSE Class 12 Linear Programming Syllabus

Before we begin telling you about the subject and help you excel in it in your coming CBSE Class 12 Boards exam, it is necessary for you to understand the depth, nuances and Syllabus of CBSE Class 12 Linear programming. It is essential for you to thoroughly study the syllabus of Class 12 Linear programming. The Preparation for any exam, Linear programming included, cannot be done without the knowledge of its Syllabus.

Class 12 Linear programming Syllabus comprises topics that become a cornerstone to your Linear Programming taught in college-level and higher studies. You might be familiar with Some of the topics. Whereas, some will be alien to you. However, the topics that are new to you will have applications from what you have already studied up to your Class 11. Some of the topics covered in Linear programming are Constraints, Mathematical Formulation and Feasible Regions and Graphs.

Let us look at Class 12 Linear programming syllabus in detail and find out its content

  • Introduction and related terminologies (constraints, objective function, optimization)
  • 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)

We cannot stress enough on the significance of Class 12 Linear Programming Syllabus. You are suggested to study the syllabus and spend some time with the detailed sub-topics included under the aforementioned Linear Programming Topics of Class 12. A thorough study of Syllabus of Class 12 Linear programming will help you keep a real assessment of your Linear programming CBSE preparation. You are also advised to be always up to date with the topics that you have completed and topics you still have to cover. It will keep you in your relevant topics lane and you will never deviate from the right path that contains the right topics.

CBSE Class 12 Linear Programming Weightage

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. Holding 8 marks out of the total 80 marks in your paper with over 25 periods, it is one of the subjects that you just can't miss out on.

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.

Subject

Periods

Weightage

Linear Programming

25

08/80

Thus all students are advised 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.

What to expect in the Linear Programming Exam?

Like we mentioned in our other article on CBSE Class 12 Financial Mathematics, “Syllabus is the guiding light”. It does actually stand true for every subject of CBSE Class 12. It is an undisputed fact that a student who knows the syllabus inside out has higher chances of topping the exam as compared to a student you don't know about the syllabus of the subject.

Let us figure out what the subject of Linear programming expects from you. And how you are expected to approach problems of the subject to score full marks in it. CBSE Class 12 Applied Mathematics (Linear programming) expects you to inculcate mathematical language and symbolism. This is encouraged for you to communicate and relate everyday experiences mathematically. So that you are able to understand the concepts and their utility in a much more profound way.

During your Class 12 Home and Pre Boards and CBSE Class 12 Board examinations, you should be ready for some questions based on logic and algorithms. While some of the questions 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 textbooks exercises and reference books examples.

The purpose of questions in CBSE Class 12 Linear programming exam is to test your adaptability to solve logics and form algorithms. You should not be afraid of dealing with complex situations in questions. You should be agile and vigilant for any errors on the part of your calculation.

In addition, the subject intends you to reinforce the logical reasoning skills. You are required to formulate and validate mathematical arguments, frame examples, find counterexamples and others. You will be engaged in mathematical investigations throughout the exam. You might be to build connections within mathematical topics and with other disciplines of real life.

Linear programming sees the application of mathematics in other fields too. Wikipedia goes on to throw more light on the subject and defines it as a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half-spaces, each of which is defined by a linear inequality.

By the time you are through with the subject, you will understand the basics of Linear programming. You will know how to find the best outcome for any event. you will also be able to form algorithms and logics for calculating the best outcome. You will learn more about vectors, matrix, coefficients, planning, routing, scheduling, assignment, and design.

How to Prepare for the Linear programming Exam?

How you score in your Class 12 Applied Mathematics Linear programming test depends on how you prepare for it. How you Prepare for the subject depends on what your CBSE Class 12 Linear programming Preparation Strategy is. We are discussing the most important points that you should consider while preparing for CBSE Class 12 Linear programming. Some of the major guidelines for your Preparation are mentioned below:

Follow the Syllabus: CBSE Class 12 Linear Programming Syllabus is of the utmost importance when it comes to preparation of Linear programming. You should regularly take guidance from the syllabus while preparing for your Linear programming subject. Let the CBSE Class 12 Linear Programming syllabus be your guiding light in the journey towards acing CBSE 12 Linear Programming.

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. Practising 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 NCERTyou can graduate to a reference book. Please note that this should be done after completing the NCERT Linear Programming Textbook and not before it.

Practise Previous Year papers: this is equally important as CBSE 12 Applied mathematics Linear Programming Syllabus if not more. Linear programming NCERT Previous Year papers will help you with the NCERT Linear Programming Exam Pattern and trends of questions asked in the examination. Solving Linear programming PYQs 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 become at it. It helps with your calculation skills and mental storage capacity. Which in turn helps you in solving even bigger and more complex questions later.

Study Material for Linear programming

In your journey towards acing any exam, Books/ Notes are your truest friend and mock papers are your biggest cheerleaders.

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. Text Books, Reference Books, clubbed with your syllabus is your ultimate weapon in the examination. Let us take a look at the list of reference books you should be reading/ studying while preparing for the Linear Programming Exam.

Sample Questions for CBSE Class 12 Linear Programming

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 found a few questions from most topics to help you understand the type of question and knowledge that a Financial Mathematics Exam at Standard XI expects from you.

  1. : Solve the following LPP graphically:

Maximise Z = 2x + 3y, subject to x + y ≤ 4, x ≥ 0, y ≥ 0

Q: 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

  1. A manufacturing company makes two types of television sets; one is black and white and the other is colour. 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 coloured 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 coloured 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 maximise the profit.
  2. 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 minimise the cost of such a mixture.
  3. 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.

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.

Sample Paper for CBSE Class 12 Linear programming

Linear Programming Sample papers are the best resource for practising for subjects such as Maths. Experts including, book authors, school teachers, university lecturers come together to form sample papers for students to practise.

By solving CBSE class 12 Linear programming Sample Papers, students will get clearer ideas regarding the exam pattern, level of difficulty, types of questions asked in the Linear Programming Examination. This will help them gauge their preparation and make according to adjustments to their strategy

Hence, it is advisable for you to keep a regular flow of practice sessions with sample papers in your Financial Mathematics preparation strategy and ace the exam later on

FAQ's

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.