# NCERT Solutions for Class 12 Maths Chapter 12

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming (LPP) Exercise 12.1, 12.2 & miscellaneous exercises in PDF form to free download updated for new academic session 2020-2021.

NCERT Text books and their solutions, CBSE syllabus for current year 2020-21, previous year board papers for practice and assignments, tests, revision books all in PDF. Share your views through Discussion Forum.## NCERT Solutions for Class 12 Maths Chapter 12

Class: | 12 |

Subject: | Maths |

Chapter 12: | Linear Programming |

### 12th Maths Chapter 12 Solutions

NCERT Solutions for Class 12 Maths Chapter 12 in PDF form to free download updated for new academic year 2020-2021. NCERT Books 2020-21 and Offline Apps are for all boards following CBSE Syllabus. Join the discussion forum to ask your doubts in NIOS and CBSE Board.

### Chapter 12 Solutions in PDF

- Download Exercise 12.1 in PDF
- Download Exercise 12.2 in PDF
- Download Miscellaneous Exercise 12
- NCERT Book Chapter 12
- NCERT Book Answers
- Revision Book Chapter 12
- Revision Book Answers
- Download Assignment 1
- Download Assignment 2
- Download Assignment 2 Answers
- Download Assignment 3
- Download Assignment 4
- Visit to 12th Maths Main Page

#### Important Questions for practice

1. 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]

2. 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]

##### Questions from Board Papers

1. 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]

2. 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]

3. 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]