Linear Programming

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New question posted•a year ago

Linear Programming Maths NCERT Exemplar Solutions Class 12th Chapter Twelve

<p><strong>In a LPP, the linear inequalities or restrictions on the variables are called __________.</strong></p>

3 Views|Posted a year ago

Asked by Payal Gupta

New answer posted•a year ago

Linear Programming Maths NCERT Exemplar Solutions Class 12th Chapter Twelve

The number of elements in the set ${z = a + i b \in C : a, b \in Z a n d 1 < | z - 3 + 2 i | < 4}$ is

15 Views|Posted a year ago

Asked by Payal Gupta

Answered by

Payal Gupta | Contributor-Level 10

a year ago

$1 < | z - 3 + 2 i | < 4$

$z = a + i b a, b \in I$

⇒ 1 < (a – 3)² + (b + 2)² < 16

in equivalent to 1 < α² + β² < 16 $α = a - 3 \in l$

$(\pm 2, 0) (\pm 3, 0), (0, \pm 2) (0, \pm 3)$ $β = b + 2 \in l$

Total 40 such points are possible

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New answer posted•a year ago

Linear Programming Class 12th

31. A toy company manufactures two types of dolls, A and B. Market research and available resources have indicated that the combined production level should not exceed 1200 dolls per week, and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other types by at most 600 units. If the company makes a profit of ?. 12 and ?. 16 per doll on dolls A and B, respectively, how many of each should be produced weekly in order to maximise the profit?

5 Views|Posted a year ago

Asked by Vishal Baghel

Answered by

Vishal Baghel | Contributor-Level 10

a year ago

Let x and y be the number of dolls of type A and B, respectively, that are produced in a week.

The given problem can be formulated as given below:

$M a x i m i s e z = 12 x + 16 y \dots \dots \dots . . (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} x + y \leq 1200 \dots \dots \dots \dots (i i)$

$y \leq x / 2 o r x \geq 2 y \dots \dots \dots . (i i i)$

$x- 3 y \leq 600 \dots \dots \dots \dots . (i v)$

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

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

A (600, 0), B (1050, 150) and C (800, 400) are th

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New answer posted•a year ago

Linear Programming Class 12th

30. Refer to Question 8. If the grower wants to maximise the amount of nitrogen added to the garden, how many bags of each brand should be added? What is the maximum amount of nitrogen added?

7 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:

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

Subject to the constraints,

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

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

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

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

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

A (140, 50), B (20, 140) and C (40, 100) are the corner points of the

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New answer posted•a year ago

Linear Programming Class 12th

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

Linear Programming Class 12th

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

Linear Programming Class 12th

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

Linear Programming Class 12th

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

Linear Programming Class 12th