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NCERT Solutions for Exercise 12.2 Class 12 Maths Chapter 12 Linear Programming are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. NCERT solutions for exercise 12.2 Class 12 Maths chapter 12 discuss a few types of linear programming problems. There are 11 practice questions given in exercise 12.2 Class 12 Maths. All these problems of NCERT solutions for Class 12 Maths chapter 12 exercise 12.2 are done using graphical methods. Manufacturing problems, diet problems, transportation problems are some of the linear programming problems given in the Class 12 Maths chapter 12 exercise 12.2. According to the given statements, the given objective functions and the constraints are formulated and then solved using graphical methods. Along with the Class 12 Maths chapter 12 exercise 12.2 solutions there are two more exercises.
All these NCERT problems are solved by Mathematics expert faculties and NCERT solutions for Class 12 Maths chapter 12 exercise 12.2 can be used for the preparation of the CBSE Class 12 Board Exam. 12th class Maths exercise 12.2 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise enumerated in NCERT Book together using the link provided below.
Answer:
Let mixture contain x kg of food P and y kg of food Q. Thus, .
The given information can be represented in the table as :
Vitamin A | Vitamin B | Cost | |
Food P | 3 | 5 | 60 |
Food Q | 4 | 2 | 80 |
requirement | 8 | 11 |
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
The mixture must contain 8 units of Vitamin A and 11 units of Vitamin B.
Therefore, we have
Total cost is Z.
Subject to constraint,
The feasible region determined by constraints is as follows:
It can be seen that a feasible region is unbounded.
The corner points of the feasible region are
The value of Z at corner points is as shown :
corner points | ||
160 | MINIMUM | |
160 | minimum | |
440 |
Feasible region is unbounded, therefore 160 may or may not be the minimum value of Z.
For this, we draw and check whether resulting half plane has a point in common with the feasible region or not.
We can see a feasible region has no common point with.
Hence, Z has a minimum value 160 at line segment joining points and .
Answer:
Let there be x cakes of first kind and y cakes of the second kind.Thus, .
The given information can be represented in the table as :
Flour(g) | fat(g) | |
Cake of kind x | 200 | 25 |
Cake of kind y | 100 | 50 |
Availability | 5000 | 1000 |
Therefore,
.
The total number of cakes, Z. Z=X+Y
Subject to constraint,
The feasible region determined by constraints is as follows:
The corner points of the feasible region are
The value of Z at corner points is as shown :
corner points | Z=X+Y | |
25 | ||
30 | maximum | |
20 0 | minimum |
The maximum cake can be made 30 (20 of the first kind and 10 of the second kind).
(i) What number of rackets and bats must be made if the factory is to work at full capacity?
Answer:
Let number of rackets be x and number of bats be y.
the machine time availability is not more than 42 hours.
i.e.
craftsman’s time availability is 24 hours
i.e.
The factory has to work at full capacity.
Hence,
Solving equation 1 and 2, we have
Thus, 4 rackets and 12 bats are to be made .
(ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.
Answer:
Let the number of rackets is x and the number of bats is y.
the machine time availability is not more than 42 hours.
craftsman’s time availability is 24 hours
The given information can be repreented in table as shown :
racket | bat | availability | |
machine time | 1.5 | 3 | 42 |
craftman's time | 3 | 1 | 24 |
The profit on the bat is 10 and on the racket is 20.
The mathematical formulation is :
maximise
subject to constraints,
The feasible region determined by constraints is as follows:
The corner points are
The value of Z at corner points is as shown :
CORNER POINTS | ||
160 | ||
200 | maximum | |
140 | ||
0 |
Thus, the maximum profit of the factory when it works at full capacity is 200.
Answer:
Let packages of nuts be x and packages of bolts be y .Thus, .
The given information can be represented in table as :
bolts | nuts | availability | |
machine A | 1 | 3 | 12 |
machine B | 3 | 1 | 12 |
Profit on a package of nuts is Rs. 17.5 and on package of bolt is 7.
Therefore, constraint are
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
Corner points | ||
70 | ||
73.5 | maximum | |
28 | ||
0 |
The maximum value of z is 73.5 at .
Thus, 3 packages of nuts and 3 packages of bolts should be manufactured everyday to get maximum profit.
Answer:
Let factory manufactures screws of type A and factory manufactures screws of type B. Thus, .
The given information can be represented in the table as :
screw A | screw B | availability | |
Automatic machine | 4 | 6 | |
hand operated machine | 6 | 3 | |
Profit on a package of screw A is Rs.7 and on the package of screw B is 10.
Therefore, the constraint is
The feasible region determined by constraints is as follows:
The corner points of the feasible region are
The value of Z at corner points is as shown :
Corner points | ||
280 | ||
410 | maximum | |
400 | ||
0 |
The maximum value of z is 410 at .
Thus, 30 packages of screw A and 20 packages of screw B should be manufactured every day to get maximum profit.
Answer:
Let the cottage industry manufactures x pedestal lamps and y wooden shades. Thus, .
The given information can be represented in the table as :
lamps | shades | availability | |
machine (h) | 2 | 1 | 12 |
sprayer (h) | 3 | 2 | 20 |
Profit on a lamp is Rs. 5 and on the shade is 3.
Therefore, constraint is
The feasible region determined by constraints is as follows:
The corner points of the feasible region are
The value of Z at corner points is as shown :
Corner points | ||
30 | ||
32 | maximum | |
30 | ||
0 |
The maximum value of z is 32 at .
Thus, 4 shades and 4 pedestals lamps should be manufactured every day to get the maximum profit.
Answer:
Let x be Souvenirs of type A and y be Souvenirs of type B .Thus, .
The given information can be represented in table as :
Type A | Type B | availability | |
cutting | 5 | 8 | |
asembling | 10 | 8 | |
Profit on type A Souvenirs is Rs. 5 and on type B Souvenirs is 6.
Therefore, constraint are
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
Corner points | ||
120 | ||
160 | maximum | |
150 | ||
0 |
The maximum value of z is 160 at .
Thus,8 Souvenirs of type A and 20 Souvenirs of type B should be manufactured everyday to get maximum profit.
Answer:
Let merchant plans has personal computers x desktop model and y portable model
.Thus, .
The cost of desktop model is cost Rs 25000 and portable model is Rs 40000.
Merchant can invest Rs 70 lakhs maximum.
the total monthly demand of computers will not exceed 250 units.
profit on the desktop model is Rs 4500 and on portable model is Rs 5000.
Total profit = Z ,
The mathematical formulation of given problem is :
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
Corner points | ||
1125000 | ||
1150000 | maximum | |
875000 | ||
0 |
The maximum value of z is 1150000 at .
Thus, merchant should stock 200 desktop models and 50 portable models to get maximum profit.
Answer:
Let diet contain x unit of food F1 and y unit of foof F2 .Thus, .
The given information can be represented in table as :
Vitamin | minerals | cost per unit | |
foof F1 | 3 | 4 | 4 |
food F2 | 6 | 3 | 6 |
80 | 100 |
Cost of food F1 is Rs 4 per unit and Cost of food F2 is Rs 6 per unit
Therefore, constraint are
The feasible region determined by constraints is as follows:
We can see feasible region is unbounded.
The corner points of feasible region are
The value of Z at corner points is as shown :
Corner points | ||
106.67 | ||
104 | minimum | |
200 | maximum | |
Feasible region is unbounded , therefore 104 may or may not be minimum value of Z .
For this we draw or and check whether resulting half plane has point in common with feasible region or not.
We can see feasible region has no common point with .
Hence , Z has minimum value 104.
Answer:
Let farmer buy x kg of fertilizer F1 and y kg of F2 .Thus, .
The given information can be represented in table as :
Nitrogen | phosphoric acid | Cost | |
F1 | 10 | 6 | 6 |
F2 | 5 | 10 | 5 |
requirement | 14 | 14 |
F1 contain 10% nitrogen and F2 contain 5% nitrogen .Farmer requires atleast 14 kg of nitrogen
F1 contain 6% phophoric acid and F2 contain 10% phosphoric acid .Farmer requires atleast 14 kg of nitrogen
Total cost is Z .
Subject to constraint ,
The feasible region determined by constraints is as follows:
It can be seen that feasible region is unbounded.
The corner points of feasible region are
The value of Z at corner points is as shown :
corner points | ||
1400 | ||
1000 | minimum | |
1400 |
Feasible region is unbounded , therefore 1000 may or may not be minimum value of Z .
For this we draw and check whether resulting half plane has point in common with feasible region or not.
We can see feasible region has no common point with .
Hence , Z has minimum value 1000 at point
Question:11 The corner points of the feasible region determined by the following system of linear inequalities:
are and . Let where Condition on p and q so that the maximum of Z occurs at both and is
Answer:
The maximum value of Z is unique.
It is given that maximum value of Z occurs at two points .
Value of Z at =value of Z at
Hence, D is correct option.
Before exercise 12.2 Class 12 Maths, there are 3 solved examples. The first examples are diet, allocation and manufacturing problems. The Class 12 Maths chapter 12 exercise 12.2 have 11 problems out of which 1 is a multiple-choice question. After exercise 12.2 there are miscellaneous examples and exercises for practice.
Also Read| Linear Programming Class 12th Notes
By solving the Class 12 Maths NCERT syllabus chapter 12 exercise 2 problems students will be able to clarify their doubts in the concepts covered in the chapter and will be helpful for exams also
Some of the linear programming problems are diet problems, manufacturing problems, allocation problems and transportation problems
The number of products which should be produced and sold is determined here subjected to some constraints like manpower, machines, labour etc
Diet problems minimise the cost of diet subjected to the amount of different nutrients required
Students may get up to 5 marks questions from the Class 12 NCERT chapter linear programming
No, exercise 12.1 explains the method of solving linear programming problems using graphs. Once students are through with the first exercise they can move to the second one. The concepts covered in the first exercise are used to solve the second exercise.
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It's understandable to feel disheartened after facing a compartment exam, especially when you've invested significant effort. However, it's important to remember that setbacks are a part of life, and they can be opportunities for growth.
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Hi,
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hello mahima,
If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.
hope this helps.
Hello Akash,
If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.
You can get the Previous Year Questions (PYQs) on the official website of the respective board.
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
Hello student,
If you are planning to appear again for class 12th board exam with PCMB as a private candidate here is the right information you need:
Remember
, these are tentative dates based on last year. Keep an eye on the CBSE website ( https://www.cbse.gov.in/ ) for the accurate and official announcement.
I hope this answer helps you. If you have more queries then feel free to share your questions with us, we will be happy to help you.
Good luck with your studies!
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