CBSE Class 12th Mathematics Chapter 12 - Linear Programming Important Questions with Answers

You should focus on solving CBSE Class 12th Mathematics Chapter 12: Linear Programming important questions, especially to help you score high marks. By solving CBSE Class 12th Mathematics 12 questions, you will be solving exam-oriented questions only.

Never Miss an Exam Update

CBSE Class 12th Mathematics Chapter 12 - Linear Programming is a chapter in the V unit of the syllabus. This chapter will carry 20 periods and 5 marks. There are a total of 6 units included in the Mathematics syllabus according to the Central Board of Secondary Education and each unit carries different chapters. The theory paper in Mathematics will be conducted for 80 marks and 20 marks will be provided for internal assessment/project work. Mathematics can be an intimidating subject, it is advised to complete the syllabus as soon as possible and understand the curriculum to further work on practice. In Mathematics, it is important to regularly solve sums and problems to be confident enough while solving them during the board exams.

Chapter 12 will include the following topics: Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints). For revising, you can easily download the sample question papers available on the official website of CBSE Academics. You can also download the previous year's question papers uploaded on the official website to help the students learn about the commonly asked topics and problems. Further, you can also take mock tests available on the internet and assess your preparation level by checking your score.

The Central Board of Secondary Education has already released the class 12th date sheet on the official website in a PDF format. You can use it to check the exam dates. The CBSE Class 12 Mathematics Basic Paper is on Saturday, March 8, 2025, from 10:30 AM to 1:30 PM. The Applied Mathematics Paper will also be held on the same day and time. To prepare for the exam thoroughly, you can check out the questions mentioned below. Try solving these questions and then you can also check the answers by clicking on the tab. Refer to the CBSE Class 12th Mathematics Chapter 12 - Linear Programming Important Questions with Answers here:

Are you feeling lost and unsure about what career path to take after completing 12th standard?

Say goodbye to confusion and hello to a bright future!

Was this article helpful?

0 Upvotes

0 Downvotes

A manufacturer has employed 5 skilled men and 10 semi-skilled men and makes two models A and B of an article. The making of one item of model A requires
2 h work by a skilled man and 2 h work by a semi-skilled man. One item of model B requires 1 h by a skilled man and 3 h by a semi-skilled man. No man is expected to work more than 8 h per day. The manufacturer profit on an item of model A is t 15 and on an items of model B is ? 10. How many of items of each models should be made per day in order to maximize daily profit? Formulate the above LPP and solve it graphically and find the maximum profit. (Delhi 2019)

Question 2.

A company produces two types of goods, A and B, that require gold and silver. Each unit of type A requires 3 g of silver and 1 g of gold while that of type B requires 1 g of silver and 2 g of gold. The company can use at the most 9 g of silver and 8 g of gold. If each unit of type A brings a profit of ? 40 and that of type B ? 50, find the number of units of each type that the company should produce to maximize profit. Formulate the above LPP and solve it graphically and also find the maximum profit. (All India 2019, CBSE 2018C)

Question 3.

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ? 100 and that on a bracelet is ? 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximise the profit? It is being given that at least one of each must be produced. (Delhi 2017)

Question 4.

Two tailors A and B, earn ? 300 and ? 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP. (All India 2017 )

Question 5.

Solve the following LPP graphically:
Minimise Z = 5x + 10y subject to the constraints
x + 2y ? 120
x + y ? 60,
x – 2y > 0 and x, y ? 0 (Delhi 2017)

Question 6.

Maximise and minimise Z = x + 2y subject to the constraints
x + 2 y ? 100
2x – y ? 0
2x+ y ? 200
x, y ? 0
Solve the above LPP graphically. (All India 2017)

Question 7.

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 h and that of second machine is 9 h per day. Each unit of product A requires 3 h on both machines and each unit of product B requires 2 h on first machine and 1 h on second machine. Each unit of product A is sold at a profit of ? 7 and B at a profit of ? 4. Find the production level per day for maximum profit graphically. (Delhi 2016)

Question 8.

A retired person wants to invest an amount of ? 50000. His broker recommends investing in two types of bonds A’ and ‘B’ yielding 10% and 9% return respectively on the invested amount. He decides to invest at least ? 20000 in bond A’ and at least ? 10000 in bond ‘B’. He also wants to invest at least as much in bond A’ as in bond ‘B’. Solve this linear programming problem graphically to maximise his returns. (All Indio 2016)

Question 9.

There are two types of fertilisers A and B’. A’ consists of 12% nitrogen and 5% phosphoric acid whereas B’ consists of 4% nitrogen and 5% phospheric acid. After testing the soil conditions, farmer finds that he needs at least 12 kg of nitrogen and 12 kg of phosphoric acid for his crops. If‘A’ costs 110 per kg and B’ costs ? 8 per kg , then graphically determine how much of each type of fertiliser should be used so that the nutrient requirements are met at a minimum cost? (All India 2016)

Question 10.

In order to supplement daily diet, a person wishes to take X and Y tablets. The contents (in milligrams per tablet) of iron, calcium and vitamins in X and Y are given as below:
Linear Programming Class 12 Maths Important Questions Chapter 12 16

Linear Programming Class 12 Maths Important Questions Chapter 12 16

The person needs to supplement at least 18 milligrams of iron, 21 milligrams of calcium and 16 milligrams of vitamins. The price of each tablet of X and Y is ? 2 and ? 1, respectively. How many tablets of each type should the person take in order to satisfy the above requirement at the minimum cost? Make an LPP and solve graphically. (Foreign 2016)

Question 1.

A manufacturer produces nuts and bolts. It take 2 hours work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 2 hours on machine B to produce a package of bolts. He earns a profit of ? 24 per package on nuts and ? 18 per package on bolts. How many package of each should be produced each day so as to maximise his profit, if he operates his machines for at most 10 hours a day? Make an LPP and solve it graphically. (All India 2015C)

Question 2.

Find graphically, the maximum value of Z = 2x + 5y, subject to constraints given below
2x+ 4y ? 8; 3x + y ? 6
x + y ? A; x ? 0, y ? 0. (Delhi 2015)

Question 3.

Maximise Z = 8x + 9y subject to the constraints given below:
2x + 3y ? 6 3x – 2y ? 6
y ? 1; x,y ? 0. (Foreign 2015)

Question 4.

One kind of cake requires 200 g of flour and 25 g of fat, 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 it as an LPP and solve it graphically. (Delhi 2015C; All India 2014C, 2011C)

Question 5.

A dealer in rural area wishes to purchase a number of sewing machines. He has only ? 5760 to invest and has space for atmost 20 items for storage. An electronic sewing machine cost ? 360 and a manually operated sewing machine ? 240. He can sell an electronic sewing machine at a profit of ? 22 and a manually operated sewing machine at a profit of ? 18. Assuming that he can sell all the items that he can buy, how should he invest his money in oder to maximise his profit? Make it as an LPP and solve it graphically. (Delhi 2014,2009C; All India 2009)

Question 6.

A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30, respectively. The company makes a profit of t 80 on each piece of type A and ? 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week? (All India 2014)

Question 7.

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 h on the grinding/cutting machine and 3 h on the sprayer to manufacture a pedestal lamp. It takes 1 h on the grinding/cutting machine and 2 h on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 h and the grinding/cutting machine for at most 12 h. The profit from the sale of a lamp is ? 25 and that from a shade is ? 15. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit? Formulate an LPP and solve it graphically. (Foreign 2014)

Question 8.

A decorative item dealer deals in two items A and B. He has ? 15000 to invest and a space to store at the most 80 pieces. Item A costs him ? 300 and item B costs him ? 150. He can sell items A and B at respective, profits of ? 50 and ? 28. Assuming he can sell all he buys, formulate the linear programming problem in order to maximise his profit and solve it graphically. (Delhi 2012C)

Question 9.

A manufacturer produces nuts and bolts.
It takes 1 h of work on machine A and 3 h on machine B to produce package of nuts. It takes 3 h on machine A and 1 h on machine B to produce a package of bolts. He earns a profit of ? 17.50 per package : on nuts and ? 7 per package on bolts. How many packages of each should be produced each day so as to maximise his profits, if he operates his machines for atmost 12 h a day? Formulate above as a Linear Programming Problem (LPP) and solve it graphically. (Delhi 2012,2009C)

Question 10.

A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 1 hours on machine B to produce a package of nuts while it takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of ? 2.50 per package of nuts and ? 1.00 per package of bolts. How many packages of each type should he produce each day so as to maximise his profit, if he operates his machines for at most 12 hours a day? Formulate this problem as a linear programming problem and solve it graphically. (All India 2012C)