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.
© Copyright 2011 - 12 Educomp Solutions Ltd. Page 4 of 6

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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