(linear programming problem) graphically by using iso

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Question: 1.

Solve the following LPP (linear programming problem) graphically by using iso-profit method

Maximize Z=50x+ 10y

Subject to x+y < 30

4x+y < 80

x, y > 0

Question: 2.

For the following LPP:

Maximize Z=7x+ 9y

Subject to x +y < 6

5x+9y < 45

8x+3y < 24

x, y > 0

What is the point at which the maximum of Z is obtained?

Question: 3.

Solve the following LPP ( linear programming problem) graphically by using iso-profit method

Minimize Z=4x+ 7y

Subject to -3x+y < 6

x+y > 5

x-2y < 4

x, y > 0

Question: 4.

Solve the following LPP ( linear programming problem) graphically by using iso-profit method

Minimize Z= x y

20 20

Subject to 6x+5y > 30

4x+5y > 20

x, y > 0

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Question: 5.

Solve the following LPP ( linear programming problem) graphically by using iso-profit method

Minimize Z= 30x+50y

Subject to 25x+5y > 100

6x+12y > 60

30x+20y > 240

x, y > 0

Question: 6.

Solve the following LPP ( linear programming problem) graphically by using iso-profit method

Minimize Z=

2 x y

5 5

Subject to x+y > 200

2x+4y > 600

x, y > 0

Question: 7.

Solve the following LPP ( linear programming problem) graphically by using iso-profit method

Maximize Z= 40x + 50y

Subject to 4x+7y < 280

10x+5y < 200

x, y > 0

Question: 8.

Solve the following LPP ( linear programming problem) graphically by using iso-profit method

Maximize Z= 2x + 3y

Subject to 3x+3y < 420

6x+3y < 540

x, y > 0

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Question: 9.

Solve the following LPP ( linear programming problem) graphically by using iso-profit method

Minimize Z= 0.40x +y

Subject to 10x+3y > 30

4x+4y > 20

2x+7y > 14

x, y > 0

Question: 10.

Solve the following LPP (linear programming problem) graphically by using iso-profit method

Maximize Z= 20x + 15y

Subject to 3x+ y < 60

3x+4y < 120

x, y > 0

Question: 11.

Solve the following LPP ( linear programming problem) graphically by using iso-profit method

Maximize Z= 10x + 15y

Subject to

5x+ 10y < 50

4x+4y < 24

x, y > 0

Question: 12.

For the following data:

Product

P

Q

Nutrient

Constituents

Cost in $

A B

C

10 4

3

10

30

5 12

6

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Minimum

Requirement

50 24

18

Formulate a LPP to minimize the total cost and solve it by iso-profit method.

Question: 13.

A dealer wishes to purchase a number of fans and sewing machines. He has $3200 to invest and has space for atmost 50 items. A Fan cost him $40 and sewing machine $ 80. He wants to sell a fan at a profit of $20 and sewing machine at $15.

Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize profit. Solve this problem using iso-profit method of Linear

Programming.

Question: 14.

Solve the following LPP ( linear programming problem) graphically by using iso-profit method

Maximize Z= 50x + 30y

Subject to 12x+ 6y < 72

1000x+ 1400y < 7000

x, y > 0

Question: 15.

Solve the following LPP ( linear programming problem) graphically by using iso-profit method

Maximize Z= 3x + 5y

Subject to 6x+ 6y < 420

5x+9y < 450

x, y > 0

Question: 16.

A manufacturer makes two types A and B of containers two machines are needed for the manufacturer and the time in minutes required for each container on the machines is given as:

Machines

I II

A 9 6

B 4 6

Each machine is available for a maximum of 6 hours/day. If the profit on each container A is $ 3 and that on each container B is $2, find the number of containers of each type that should be manufactured to maximize the profit what is the maximum profit.

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Question: 17.

Solve the following LPP (linear programming problem) graphically by using iso-profit method

Maximize Z= 40x + 30y

Subject to 500x+ 800y < 4000

10x+ 7y < 70

x, y > 0

Question: 18.

Solve the following LPP ( linear programming problem) graphically by using iso-profit method

Minimize Z= 6x +9y

Subject to x + y > 8

x+4y > 12

2x+y > 10

x, y > 0

Question: 19.

Solve the following LPP (linear programming problem) graphically by using iso-profit method

Maximize Z = 0.8x + 0.5y

Subject to 5x+ 6y < 300

10x+ 5y < 300

x, y > 0

Question: 20.

Solve the following LPP (linear programming problem) graphically by using iso-profit method

Maximize Z = 0.85x + 0.25y

Subject to 16x+ 8y < 480

24x+ 6y < 480

6x+ 8y < 480

x, y > 0

© Copyright 2011 - 12 Educomp Solutions Ltd. Page 5 of 6

Answers:

A1.

Maximum value of Z = 1000

A2.

x

27

, y

19

80

19

A3.

Minimum value of Z = 21

A4.

Minimum value of Z = 0.25

A5.

Minimum value of Z = 285 at x= 7 and y = 3/2

A6.

Minimum value of Z = 40 at x= 0 and y = 200

A7.

Maximum value of Z = 2000 at x= 0 and y = 40

A8.

Maximum value of Z = 420 at x= 0 and y = 140

A9.

Minimum value of Z = 2.48 at x= 21/5 and y = 4/5

A10.

Maximum value of Z = 400 at x= 20 and y = 0

A11.

Maximum value of Z = 80 at x= 2 and y = 4

A12.

Minimum cost = $60 at 6 units of product P and 0 units of product Q

A13.

A dealer should purchase 50 fans and 0 sewing machines to get a maximum profit of

$1000.

A14.

Maximum value of Z = 305.6 at x= 49/9 and y = 10/9

A15.

Maximum value of Z = 260 at x= 45 and y = 25

A16.

Type A = 24, Type B = 26, maximum profit = $144

A17.

Maximum value of Z = 282.2 at x= 56/9 and y = 10/9

A18.

Minimum value of Z = 52 at x= 20/3 and y = 4/3

A19.

Maximum value of Z = 28.3 at x= 60/7 and y = 300/7

A20.

Maximum value of Z = 18.5 at x= 10 and y = 40

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