NCERT Solutions for Class 12 Maths Chapter 12

NCERT Solutions for Class 12 Maths Chapter 12 Exercise 12.1, 12.2 & miscellaneous exercises of Linear Programming (LPP) in PDF form to free download. NCERT Text books and their solutions, CBSE syllabus for current year 2019-20, previous year board papers for practice and assignments, tests, revision books all in PDF. Share your views through Discussion Forum.

Subject:Maths – गणित
Chapter 12:Linear Programming

NCERT Solutions for Class 12 Maths Chapter 12

NCERT Solutions for Class 12 Maths Chapter 12

Click Here to Class 12 Maths Main Page

Solutions of NCERT exercises given in the chapter

NCERT Chapter to study online and answers given in the end of ncert books.

These books are very good for revision and more practice. These book are also confined to NCERT Syllabus.

Assignments for practice

Level 1 Test 1

Level 2 Test 1

Previous year’s questions

  • Solve the following L.P.P. graphically:
    Minimise Z = 5x + 10y, Subject to constraints x + 2y < 120, x – 2y > 60, x – 2y > 0 and x, y >0. [Delhi 2017]
  • If a 20 year old girl drives her car at 25 km/h, she has to spend ₹ 4/km on petrol. If she drives her car at 40 km/h, the petrol cost increases to ₹ 5/km. She has ₹ 200 to spend on petrol and wishes to find the maximum distance she can travel within one hour. Express the above problem as a Linear Programming Problem. Write any one value reflected in the problem. [CBSE Sample Paper 2017]
  • A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at ₹ 7 profit and that of B at a profit of ₹4. Find the production level per day for maximum profit graphically. [Delhi 2016]

  • One kind of cake requires 200 g of flour and 25 g of fat, and another kind of cake requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes. Make an L.P.P. of the above and solve it graphically. [Delhi 2015C]
  • Find graphically, the maximum value of z = 2x + 5y, subject to constraints given below:
    2x + 4y ≤ 8
    3x + y ≤ 6
    x + y ≤ 4
    x ≥ 0, y ≥ 0 [ Delhi 2015]

What is an Optimisation Problem in LPP?

A problem which seeks to maximise or minimise a function is called an optimisation problem.

What do you understand by LPP?

A linear programming problem (LPP) deals with the optimisation (maximisation/minimisation) of a linear function of two variables (say x and y) known as objective function subject to the conditions that the variables are non-negative and satisfy a set of linear inequalities (called linear constraints).

What is a linear objective function in LPP?

Linear function Z = ax + by, where a and b are constants, which has to be maximised or minimised is called a linear objective function.

What are decision variables in LPP?

In the objective function Z = ax + by, x and y are called decision variables.

What do you mean by constraints in LPP?

The linear inequalities or restrictions on the variables of an LPP are called constraints. The conditions x ≥ 0, y ≥ 0 are called non-negative constraints.

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