# 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.

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## 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

#### 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.