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 2018-19, previous year board papers for practice and assignments, tests, revision books all in PDF.

## 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]

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