Ncert Solutions Maths class 12th

Get insights from 2.5k questions on Ncert Solutions Maths class 12th, answered by students, alumni, and experts. You may also ask and answer any question you like about Ncert Solutions Maths class 12th

2.5k
Questions
0
Discussions
1
Active Users
65
Followers

Have a question about Ncert Solutions Maths class 12th? Ask our experts

Ask Your Question

Keep it short & simple. Type complete word. Avoid abusive language.

New answer posted•a year ago

Ncert Solutions Maths class 12th Linear Programming

29. A fruit grower can use two types of fertilisers in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table, Tests indicate that the garden needs at least 240 kg of phosphoric acid, 270 kg of potash and at most 310 kg of chlorine.

If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added to the garden?

Kg per Bag

Brand P

Brand Q

Nitrogen

3

3.5

Phosphoric acid

1

2

Potash

3

1.5

Chlorine

1.5

2

6 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Let the fruit grower use x bags of brand P and y bags of brand Q, respectively.

The problem can be formulated as given below:

$M i n i m i s e z = 3 x + 3.5 y \dots \dots \dots \dots . (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} x + 2 y \geq 240 \dots \dots \dots . . (i i)$

$x + 0.5 y \geq 90 \dots \dots . . (i i i)$

$1.5 x + 2 y \leq 310 \dots \dots \dots . . (i v)$

$x, y \geq 0 \dots \dots \dots \dots . (v)$

The feasible region determined by the system of constraints is given below:

A (240, 0), B (140, 50) and C (20, 140) are the corner points of the f

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Linear Programming

28. An oil company has two depots, A and B, with capacities of 7000 L and 4000 L, respectively. The company has to supply oil to three petrol pumps, D, E and F, whose requirements are 4500L, 3000L and 3500L, respectively. The distances (in km) between the depots and the petrol pumps are given in the following table:

Distance in (km)

From/To

A

B

D

7

3

E

6

4

F

3

2

Assuming that the transportation cost of 10 litres of oil is ?. 1 per km, how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost

5 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Let x and y litres of oil be supplied from A to the petrol pumps, D and E. So, $(7000 - x - y)$ will be supplied from A to petrol pump F.

The requirement at petrol pump D is 4500 L. Since x L are transported from depot A, the remaining (4500 – x) L will be transported from petrol pump B.

Similarly $, (3000 - y) L a n d 3500 - (7000 - x - y) = (x + y - 3500)$ &nbs

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Linear Programming

28. An oil company has two depots, A and B, with capacities of 7000 L and 4000 L, respectively. The company has to supply oil to three petrol pumps, D, E and F, whose requirements are 4500L, 3000L and 3500L, respectively. The distances (in km) between the depots and the petrol pumps are given in the following table:

Distance in (km)

From/To

A

B

D

7

3

E

6

4

F

3

2

Q7. An oil company has two depots, A and B, with capacities of 7000 L and 4000 L, respectively. The company has to supply oil to three petrol pumps, D, E and F, whose requirements are 4500L, 3000L and 3500L, respectively. The distances (in km) between the depots and the petrol pumps are given in the following table:

Distance in (km)

From/To

A

B

D

7

3

E

6

4

F

3

2

Assuming that the transportation cost of 10 litres of oil is ?. 1 per km, how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost?

14 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Let x and y litres of oil be supplied from A to the petrol pumps, D and E. So, $(7000 - x - y)$ will be supplied from A to petrol pump F.

The requirement at petrol pump D is 4500 L. Since x L are transported from depot A, the remaining (4500 – x) L will be transported from petrol pump B.

Similarly $, (3000 - y) L a n d 3500 - (7000 - x - y) = (x + y - 3500)$ &nbs

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Linear Programming

27. Two godowns, A and B, have grain capacities of 100 quintals and 50 quintals, respectively. They supply to 3 ration shops, D, E and F, whose requirements are 60, 50 and 40 quintals respectively. The cost of transportation per quintal from the godowns to the shops is given in the following table:

Transportation Cost per Quintal (in Rs)

From/To

A

B

D

6

4

E

3

2

F

2.50

3

How should the supplies be transported in order that the transportation cost is minimum? What is the minimum cost?

9 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Let godown A supply x and y quintals of grain to shops D and E.

So, $(100 - x - y)$ will be supplied to shop F.

Since x quintals are transported from godown A, the requirement at shop D is 60 quintals. Hence, the remaining (60 – x) quintals will be transported from godown B.

Similarly, (50 – y) quintals and

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Linear Programming

26. An aeroplane can carry a maximum of 200 passengers. A profit of ?. 1000 is made on each executive class ticket, and a profit of ?. 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit?

5 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Let the airline sell x tickets of executive class and y tickets of economy class, respectively.

The mathematical formulation of the given problem can be written as given below:

$M a x i m i s e z = 1000 x + 600 y \dots \dots \dots \dots (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} x + y \leq 200 \dots \dots \dots \dots \dots . . (i i)$

$x \geq 20 \dots \dots \dots \dots (i i i)$

$y - 4 x \geq 0 \dots \dots \dots \dots \dots (i v)$

$x, y \geq 0 \dots \dots \dots \dots \dots (v)$

The feasible region determined by the constraints is given below:

A (20, 80), B (40, 160) and C

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Linear Programming

25. A manufacturer makes two types of toys, A and B. Three machines are needed for this purpose, and the time (in minutes) required for each toy on the machines is given below:

Types of Toys

Machines

I

II

III

A

12

18

6

B

6

0

9

Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is ?. 7.50 and that on each toy of type B is ?. 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

6 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Let x and y toys of type A and type B be manufactured in a day, respectively.

The given problem can be formulated as given below:

$M a x i m i s e z = 7.5 x + 5 y \dots \dots \dots \dots . . (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} 2 x + y ? 60 \dots \dots \dots \dots . (i i)$

$x ? 20 \dots \dots \dots . . (i i i)$

$2 x + 3 y ? 120 \dots \dots \dots . . (i v)$

$x, y ? 0 \dots \dots \dots \dots \dots . (v)$

The feasible region determined by the constraints is given below:

A (20, 0), B (20, 20), C (15, 30) and D (0, 40) are the corner points of th

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Linear Programming

24. A dietician wishes to mix together two kinds of food, X and Y, in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg of food are given below:

Food

Vitamin A

Vitamin B

Vitamin C

X

1

2

3

Y

2

2

1

One kg of food X costs ?. 16, and one kg of food Y costs ?. 20. Find the least cost of the mixture which will produce the required diet.

20 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Let the mixture contain x kg of food X and y kg of food Y, respectively.

The mathematical formulation of the given problem can be written as given below:

$M i n i m i s e z = 16 x + 20 y \dots \dots . . (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} x + 2 y \geq 10 \dots \dots \dots \dots . (i i)$

$x + y \geq 6 \dots \dots \dots \dots (i i i)$

$3 x + y \geq 8 \dots \dots \dots \dots . (i v)$

$x, y \geq 0 \dots \dots \dots \dots (v)$

The feasible region determined by the system of constraints is given below:

A (10, 0), B (2, 4), C (1, 5) and D (0, 8) are

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Linear Programming

23. A farmer mixes two brands, P and Q of cattle feed. Brand P, costing ?. 250 per bag, contains 3 units of nutritional element A, 2.5 units of element B and 2 units of element C. Brand Q costing ?. 200 per bag, contains 1.5 units of nutritional element A, 11.25 units of element B, and 3 units of element C. The minimum requirements for nutrients A, B and C are 18 units, 45 units and 24 units, respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag. What is the minimum cost of the mixture per bag?

6 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Let the farmer mix x bags of brand P and y bags of brand Q, respectively

The given information can be compiled in a table as given below:

	Vitamin A (units/kg)	Vitamin B (units/kg)	Vitamin C (units/kg)	Cost (Rs/kg)
Food P	3	2.5	2	250
Food Q	1.5	11.25	3	200
Requirement (units/kg)	18	45	24

The given problem can be formulated as given below:

$\begin{array}{l} \end{array} M i n i m i s e z = 250 x + 200 y \dots \dots \dots \dots (i)$

$3 x + 1.5 y \geq 18 \dots \dots \dots \dots . . (i i)$

$2.5 x + 11.25 y \geq 45 \dots \dots \dots . . (i i i)$

$2 x + 3 y \geq 24 \dots \dots \dots \dots . . (i v)$

$x, y \geq 0 \dots \dots \dots . (v)$

The feasible region determined by the system of constraints is given below:

A (18, 0), B (9, 2), C (3, 6) and D (0

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Linear Programming

22. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?

7 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Let the diet contain x and y packets of foods P and Q, respectively. Hence,

x ≥ 0 and y ≥ 0

The mathematical formulation of the given problem is given below:

$M a x i m i s e z = 6 x + 3 y \dots \dots \dots \dots . . (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} 4 x + y \geq 80 \dots \dots \dots \dots . (i i)$

$x + 5 y \geq 115 \dots \dots \dots . (i i i)$

$3 x + 2 y \leq 150 \dots \dots \dots \dots (i v)$

$x, y \geq 0 \dots \dots \dots \dots \dots (v)$

The feasible region determined by the system of constraints is given below:

A (15, 20), B (40, 15) and C (2, 72) a

Upvote

New answer posted•a year ago

Ncert Solutions Maths class 12th Linear Programming

21. The corner points of the feasible region determined by the following system of linear inequalities:

$2 x + y \leq 10, x + 3 y \leq 15, x, y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). Let $Z = p x + q y$ , where p, q > 0. Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is

(A) p = q

(B) p = 2q

(C) p = 3q

(D) q = 3p

15 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

The maximum value of Z is unique.

It is given that the maximum value of Z occurs at two points, (3, 4) and (0, 5).

∴ Value of Z at (3, 4) = Value of Z at (0, 5)

$\begin{array}{l} \Rightarrow p (3) + q (4) = p (0) + q (5) \end{array}$

$\begin{array}{l} \Rightarrow 3 p + 4 q = 5 q \end{array}$

$\begin{array}{l} \Rightarrow q = 3 p \end{array}$

Hence, the correct answer is D.

Hence option (D) is correct.

Upvote

Kg per Bag
	Brand P	Brand Q
Nitrogen	3	3.5
Phosphoric acid	1	2
Potash	3	1.5
Chlorine	1.5	2

Food	Vitamin A	Vitamin B	Vitamin C
X	1	2	3
Y	2	2	1

Transportation Cost per Quintal (in Rs)
From/To	A	B
D	6	4
E	3	2
F	2.50	3

Ncert Solutions Maths class 12th

Questions

Discussions

Active Users

Followers