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Xam Idea Class 12 Maths Chapter 13 Solutions: Linear Programming

Xam Idea Class 12 Maths Solutions for Chapter 13 ‘Linear Programming’ are prepared by our subject matter experts as per the latest CBSE Class 12 exam guidelines. This chapter aims to introduce the concepts of optimization problems. It focuses on finding the maximization and minimization of various quantities, graphical methods of solving linear programming problems, different types of linear programming problems, and their mathematical formulas.

Xam Idea Class 12 Maths Solutions include 22 questions. These solutions act as an extra source to practice the problems to excel in your CBSE board exams. They cover various types of solved problems for the chapter that varies from simple to complex types. You will be able to easily solve the problems of transportation, manufacturing and diet based on linear programming with the help of our Xam Idea solutions.

If you are determined to excel in Class 12 CBSE board exams with good marks, you should refer to the Xam Idea Maths solutions provided by Instasolv. Solutions provided by our team for linear programming will help you in understanding and remembering the important topics from the board exam’s point of view. It will help you to build and develop your analytical skills to understand and solve the problems quickly and efficiently.

Important topics for Xam Idea Class 12 Maths Solutions Chapter 13 – Linear Programming

In this section, we will focus on the important topics of the chapter, linear programming.

  • Linear Programming: It is a mathematical modelling technique used to achieve maximized or minimized linear functions when subjected to various constraints. This technique is most useful in business planning and industrial engineering for making decisions.
  • Feasible Region: A region that is common to all the linear inequality constraints, is called a feasible region.
  • Constraints: The system of linear inequalities (or equalities) under which the objective function is to be optimized is called constraints.
  • Problem Constraints: Linear inequalities that are derived from the application, are called problem constraints.
  • Objective functions: The function which is to be optimized (maximized/minimized) is called an objective function.
  • Bounded region: Bounded region is a workable region that can be enclosed in a circle. A bounded region will have both maximum and minimum values.
  • Unbounded region: A feasible region that cannot be enclosed in a circle. The objective function of the unbounded region is infinite.
  • Corner Point: The vertices of the feasible region are called Corner point. When we draw the graph of the system of linear inequalities, then just by looking at the graph we can easily find out the corner point. But, not all the points at lines intersecting are corner points.
  • Linear Programming Problems: A linear programming problem consists of a linear function to be maximized or minimized subject to certain constraints in the form of linear equations or inequalities.
  • Different types of Linear Programming Problems: The various types of linear programming problems covered in this chapter are:

Manufacturing Problem: Under this, we maximize profit with the help of minimum utilization of the resources.

Diet Problem: Diet problems can be achieved if we select the set of healthy nutritive food required at minimum cost.

Transportation Problem: Transportation problems can be achieved by calculating the cheapest way of the transport of the product in minimum time.

Steps for solving linear programming problems using the corner point method:

  • Converting the word problem into a mathematical equation by using given constraints.
  • Solve the mathematical linear equation formed and plot the graph.
  • Find the feasible region and determine its corner points.
  • Evaluate the objective function at each corner point.
  • If a feasible region is bounded, then the maximum and minimum values of the objective function are obtained.
  • If a feasible region is unbounded, then the objective function has no maximum and minimum values.

 Exercise Discussion for Xam Idea Class 12 Maths Solutions Chapter 13: Linear Programming

Xam Idea Class 12 Maths Chapter 13 Linear Programming has a total of 22 problems. They are categorized into 3 sections: short questions, long questions part I and long questions part II. Long questions part II is further divided into two parts PYQ (past years’ questions) and OIQ (objective inventory questionnaires’).

Short Questions 

  • It consists of a total of 4 problems in it. Problems solved in this section are not too complex to understand or solve. 
  • Questions asked are on topics like to formulate linear programming problems to maximize profit, to formulate linear programming problems to minimize cost, and to formulate linear programming problems to minimize resources.

Long Questions Part I

  • Part I consist of 3 problems. It covers the most complex and twisted problems of the chapter that need an in-depth understanding of the concept and can’t be solved by just applying a formula. 
  • Questions asked are based on topics like to determine graphically the minimum value of the objective function and to maximize and minimize the constraints.

Long Questions part II 

  • Part II consists of 15 problems out of which 12 problems fall under the category of PYQ and 3 problems under OIQ. 
  • Problems solved in this section are complex. Questions asked are related to the topic, types of linear programming problems.

Why Use Xam Idea Class 12 Maths Solutions Chapter 13: Linear Programming by Instasolv?

  • Instasolv’s Xam Idea Solutions will assist you in strengthening the weaker sections of Maths by providing simple and understandable in-depth knowledge of concepts.
  • We advise you to revise by using Instasolv’s Xam Idea Maths solutions for your CBSE exams to score high marks.
  • Instasolv’s Xam Idea solutions are easily available and free of cost.
  • Our solutions are well-designed with step-wise answers that help you to analyze the questions and solve problems efficiently.
  • Our solutions cover all the vital topics and problems as per the Class 12 board exam point.