NCERT Solutions Class 12 Mathematics Chapter 12 Linear Programming.
The Class 12 Mathematics textbook has a total of 13 chapters. Chapter 12 is about ‘Linear Programming’ that continues after the chapter ‘Three-Dimensional Geometry’. Linear Programming, also known as ‘Linear Optimisation’, is a method to get the best outcome in a Mathematical model. Linear programming is used for attaining the most optimal solution for a problem with given constraints. In NCERT Solutions Class 12 Mathematics Chapter 12 linear programming, you learn to formulate your actual problem into a Mathematical model. It involves an objective function, linear inequalities subject to constraints. Linear programming has been generally used in optimisation for several reasons. Linear programming is currently utilised in company management, such as Production, Planning, Technology, Transportation, and other related systems.
The majority of companies would like to maximise profit and minimise costs with limited resources. NCERT Solutions Class 12 Mathematics Chapter 12 Linear Programming guides you to learn the techniques of maximising profit with minimum expenses. The characteristics of linear programming are linearity, non-negativity, finiteness, objective function, and constraints. Solutions provided quickly come in handy for completing the homework and preparing for the exams. The NCERT Solutions Class 12 Mathematics Chapter 12 focuses on helping students to make positive contributions to society by developing cost-effective methods. It also suggests how a decision-maker can employ his productive factors by selecting and allocating the resources. Thus the quality of decisions can be improved by applying Linear programming techniques.
NCERT Solutions Class 12 by Extramarks strengthen your comprehensive capabilities by helping you solve complex linear programming theories in simpler ways. NCERT Solutions Class 12 Mathematics Chapter 12 give students a solid introduction to linear programming Mathematics while studying both advantages and disadvantages of applying linear techniques to different situations under varied conditions.
Key Topics Covered In NCERT Solutions Class 12 Mathematics Chapter 12
Sometimes there can be other constraints operating outside the problem. This subject teaches you the limitations of Linear Programming as this could be applied only when all the elements related to the problem can be quantified. Studying geometry provides many basic skills and builds logical thinking, analytical reasoning and problem-solving skills. The linear programming technique provides practical solutions to such issues. NCERT Solutions Class 12 Mathematics Chapter 12 teaches you to apply the fundamental plan for any given changing conditions.
The main topics covered in NCERT Solutions for Class 12 Mathematics Chapter 12-Linear Programming are:
| Exercise |
Topic |
| 12.1 |
Introduction |
| 12.2 |
Linear Programming problems and Mathematical formulation |
| 12.3 |
A Mathematical formulation of the problems |
| 12.4 |
Graphical method of solving Linear Programming problems |
| 12.5 |
Different types of Linear Programming problems |
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Introduction
Circumstances that benefit from Linear Programming problems include quality control decisions, product mix decisions, purchasing decisions, material utilisation decisions, production planning and warehousing decisions. NCERT Solutions Class 12 Mathematics Chapter 12 attracts the attention of students to deal with optimising objectives desired in situations that involve limitations. This Mathematics equation assists in creating a beneficial situation, especially in the manufacturing sector. NCERT Solutions Class 12 Mathematics Chapter 12 guides you to find the best obtainable value with the given conditions to be solved. This is quite useful in Economics, Operations research, and Business dealing with logistics. Characteristics of linear programming are :
- Linear programming concludes that all relevant input data and parameters are known with certainty.
- Linear programming’s single objective is to maximise or minimise the quantity for optimisation that caters to variable decisions.
- It helps understand the constraints that limit the ability to achieve the goal.
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Linear Programming problems and Mathematical Formulation.
The Linear Programming method assists in achieving the best outcome in a Mathematical model. NCERT Solutions Class 12 Mathematics Chapter 12 educates the students on different forms of results such as maximum profit or the lowest cost, or the best possible price. The description of this model’s requirements is a result of linear relationships.
Types of linear programming problems:
- Diet problems: The objective function is the food intake, and constraints are specified nutritional requirements.
- Manufacturing problems: The objective function is the production rate, and constraints are work hours and the cost of the packaging material.
- Transportation problems: The objective function is transportation, and constraints are specific supply and demand patterns.
- Optimal assignment problems: The objective function is the total assignments done, and constraints are the number of employees and the work hours of each employee.
NCERT Solutions Class 12 Mathematics Chapter 12 helps you analyse various problems and get better results. The main factor of Mathematical formulations is the development of definitions of variables and the functional relationships of the variables required to model the circumstance under study. To formulate a Linear Programming model, recognise the problem data in terms of constants and parameters associated with decision variables.
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A Mathematical Formulation of the Problems.
Linear Programming is a Mathematical programming technique in which a Linear function is maximised or minimised when subjected to various constraints. NCERT Solutions Class 12 Mathematics Chapter 12 explains in detail how this technique has been helpful in advising quantitative decisions in Industrial Engineering, Business Planning, Social as well as Physical Sciences. The process for the Mathematical formulation of a Linear Programming problem consists of the following steps.
- Find out the decision variable.
- Recognise the objective function to be maximised or minimised and express it as a Linear programming function of decision variables.
- Spot the set of constraint states and express them as linear inequalities or equations in terms of the decision variables.
NCERT Solutions Class 12 Mathematics Chapter 12, created by Extramarks, assists students through the process of implementing Mathematical formulas in varied industries.
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Graphical Method of Solving Linear Programming Problems gives you step-by-step Solutions to all your Queries.
NCERT Solutions Class 12 Mathematics Chapter 12 helps you calculate the Linear Programming problems for which the following steps need to be considered.
- Formulate the linear programming issue – First, you should identify the issue in an industry under the given conditions.
- Build a graph and then plot the various constraints lines – Construct a chart or diagram to show the problem points and variables governing them.
- Discover the valid side of all constraint lines: This is most important in the operations and manufacturing industry.
- Identify the region of a practical solution: Having analysed the problem, apply the best linear programming solution.
- Plot the objective function: It’s vital to know the actual problem amongst the many and develop a solution that yields the best result.
- Ultimately, find out the optimum point: Among all the variables available, it’s imperative to conclude on a perfect point.
NCERT Solutions Class 12 Mathematics Chapter 12 illustrates graphical designs which are used to formulate Mathematical functions. Various plots are used to highlight the objectives and variables.
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Different Types of Linear Programming Problems.
The different types of Linear Programming problems are Transportation, Diet, Manufacturing and Optimal Assignment Problems. NCERT Solutions Class 12 Mathematics Chapter 12 identifies the number of decision variables and expresses them in the form of Linear equations or Linear inequations.
Access NCERT Solutions Class 12 Mathematics Chapter 12 Exercises & Answer Solutions
Exercise 12.1 Solutions – 10 Questions (All Questions Require Graphs and Long Questions)
Exercise 12.2 – Linear Programming problems and Mathematical formulation – Questions & Solutions click on the link below.
Exercise 12.2 Solutions – 11 Questions (11 Questions Require Graphs and Long Questions)
Exercise 12.3 A Mathematical formulation of the problems – Questions & Solutions click here to know more.
Exercise 12.4 Graphical method of solving Linear Programming problems guides you through step-by-step solutions to the issues. – Questions & Solutions refer to the link below for further details.
Exercise 12.5 Different types of Linear Programming problems. – Questions & Solutions follow the links
Along with Class 12 Mathematics solutions, you can explore NCERT Solutions on our Extramarks website for all Primary and Secondary classes.
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NCERT Exemplars Class 12 Mathematics Chapter 12 Linear Programming.
NCERT Exemplars are practice books that include additional questions of a higher level and are meant for aiding meticulous learning. They are mainly used for competitive exams. These topics are up to date and are explained thoroughly as per the syllabus of the Class 12 Mathematics. Students can click on the links of these exemplar questions and answers provided by Extramarks for Class 12 Mathematics chapters.
Considering the standard and variety, practising exemplar problems is essential for both school boards and competitive examinations. Students can perfectly evaluate themselves by working on these problems and improving their problem-solving skills for future examinations. NCERT Solutions Class 12 Mathematics Chapter 12 provides a detailed clarification to all questions given in the NCERT Class 12 books.
Key Features of NCERT Solutions Class 12 Mathematics Chapter 12 Linear Programming
To score well in competitive exams, one should have a solid base in Mathematics. NCERT Solutions Class 12 Mathematics Chapter 12 provide you with the solutions to some of the most demanding questions that improve your analytical skills and give you sufficient exposure to any kind of questions that may be asked in board or competitive exams. Our application is extremely beneficial for your preparation for the following reasons.
- NCERT Solutions Class 12 Mathematics Chapter 12 answers to all numerical problems in the textbook and are presented in step-by-step evaluations
- Free unlimited downloads
- Highly detailed answers to all the theoretical as well as logical reasoning questions from the NCERT Mathematics textbook of Class 12 that are verified by respective experts of the subject.
- Simple and accurate answers curated by the reputed teachers cover all the difficult and straightforward topics.
- The material provided by NCERT Solutions guarantees students to score remarkably in the exams.