# NCERT Solutions for Class 12 Maths Chapter 12

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming (LPP) Exercise 12.1, 12.2 and miscellaneous exercises in Hindi and English free PDF format to download updated for new academic session 2021-2022.

NCERT Text books and their solutions, CBSE syllabus for current year 2021-22, 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 Maths Chapter 12 Solutions in Hindi and English Medium

Class: 12 | Mathematics |

Chapter: 12 | Linear Programming Problems LPP |

Contents: | Hindi and English Medium Solution |

### 12th Maths Chapter 12 Solutions

NCERT Solutions for Class 12 Maths Chapter 12 in PDF and Video format to free download in Hindi and English Medium updated for new academic year 2021-2022. Download here Class 12 Maths Offline App in English or Class 12 Maths Offline in Hindi Medium free.

### Class 12 Maths Exercise 12.1 Solution in Videos

### Class 12 Maths Exercise 12.2 Solution in Videos

#### Class 12 Maths Miscellaneous Exercise 12 Solution

#### 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]

### Important Questions on 12th Maths Chapter 12

##### 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.