# CBSE Class 12 Mathematics NCERT Exemplar Solutions: Chapter- Linear Programming

In this article, we are providing you NCERT Exemplar Solutions for all the questions of CBSE 12 Mathematics chapter 12, Linear Programming..

About NCERT Exemplar Solutions Class 12 Maths:

After the detailed analysis of some previous years’ question papers of board and engineering entrance exams, we have noticed that questions are frequently asked from NCERT Exemplar.

The experienced Subject Experts of Mathematics have explained all the questions of the chapter Inverse Trigonometric Functions in a very detailed manner to helps students to score good marks in board exams as well as competitive exams.

Questions from NCERT Exemplar Class 12 Mathematics are likely to be asked again in the board exams 2019.

CBSE Class 12 Mathematics Solved Question Paper 2018

Few problems along with their solutions from this chapter are given follows:

Q. The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y.

Compare the quantity in column A and column B.

 Column A Column B Maximum of Z 325

(a)     The quantity in column A. is greater

(b)     The quantity in column B is greater

(c)     The two quantities are equal

(d)     The relationship cannot be determined on the basis of the information supplied.

Sol. (b)

 Corner points Corresponding value of  Z = 4x+ 3y (0, 0) (0, 40) (20, 40) (60. 20) (60, 0) 0 120 200 300 (Maximum) 240

Hence, maximum value of Z = 300 < 325

So, the quantity in column B is greater.

Q. In the feasible region for a LPP is......, then the optimal value of the objective function Z = ax+by may or may not exist.

Sol.

If the feasible region for a LPP is unbounded, then the optimal value of the objective function Z =ax + by may or may not exist.

Q. In a LPP, if the objective function Z = ax +by has the same maximum value on two comer points of the feasible region, then every point on the line segment joining these

two points give the same .......... value.

Sol.

In a LPR if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same maximum value.

Find below the links to download Class 12 Mathematics NCERT Exemplar Solutions for chapter 12- Linear Programming:

About Class 12 Maths NCERT Exemplar book:

Each chapter of NCERT Exemplar Class 12 Maths book starts with a brief overview of the chapter followed by solved examples and unsolved exercises. All the problems given in this book are very important for CBSE Class 12 Maths Board examination and other engineering entrance examinations.

Main topics discussed in Class 12 Maths, Chapter 12 - Linear Programming, are:

• Linear programming problem and its mathematical formulation
• Mathematical formulation of the problem
• Graphical method of solving linear programming problems
• Different types of linear programming problems.