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# CBSE TEST PAPER-02 CLASS - XII MATHEMATICS (Linear Programming) Notes | EduRev

## : CBSE TEST PAPER-02 CLASS - XII MATHEMATICS (Linear Programming) Notes | EduRev

``` Page 1

CBSE TEST PAPER-02
CLASS - XII MATHEMATICS (Linear Programming)
Ans 01.  Let the two tailors work for x days and y days respectively
Z = 150x + 200y
6x + 10y = 60
3 5 30
4 4 32
8 and x 0, y 0
x y
x y
x y
? + =
+ =
? + = = =
Z is minimum = 1350
When A work for 5 days B work for 3 days
Ans 02.  Let P = x
Q = y
Z = 250x + 200y
3x + 1.5y = 18
2.5x + 11.25y = 45
2x + 3y = 24
x =0, y = 0
Z = Rs 1950
When x = 3 y = 6
Number of bags of brand P = 3 bags of brand Q = 6
Ans 03.  Let the dietician mix x Kg of food X and y Kg of food Y.
Z = 16x + 20y
x + 2y = 10
2x + 2y =12
6
3 8
x y
x y
? + =
+ =
Cost is minimum = 112  When 2 Kg of food X and 4 Kg of food Y are mixed.
Ans 04.  Let x toys of type A and y toys of type B
15
5
2
12 6 360
2 60
18 360
Z x y
x y
x y
x
= +
+ =
? + =
=
20
6 9 360
x
x y
? =
+ =
Page 2

CBSE TEST PAPER-02
CLASS - XII MATHEMATICS (Linear Programming)
Ans 01.  Let the two tailors work for x days and y days respectively
Z = 150x + 200y
6x + 10y = 60
3 5 30
4 4 32
8 and x 0, y 0
x y
x y
x y
? + =
+ =
? + = = =
Z is minimum = 1350
When A work for 5 days B work for 3 days
Ans 02.  Let P = x
Q = y
Z = 250x + 200y
3x + 1.5y = 18
2.5x + 11.25y = 45
2x + 3y = 24
x =0, y = 0
Z = Rs 1950
When x = 3 y = 6
Number of bags of brand P = 3 bags of brand Q = 6
Ans 03.  Let the dietician mix x Kg of food X and y Kg of food Y.
Z = 16x + 20y
x + 2y = 10
2x + 2y =12
6
3 8
x y
x y
? + =
+ =
Cost is minimum = 112  When 2 Kg of food X and 4 Kg of food Y are mixed.
Ans 04.  Let x toys of type A and y toys of type B
15
5
2
12 6 360
2 60
18 360
Z x y
x y
x y
x
= +
+ =
? + =
=
20
6 9 360
x
x y
? =
+ =
2 3 120
0, y 0
x y
x
? + =
= =
profit is maximum = 262.5 at A = 15 B = 30
Ans 05.  X passengers travel by executive class and y passengers travel by economy class. L
Z = 1000x + 600y
x + y = 200
x = 20
y = 80
x = 0, y = 0
profit is maximum = 168000
When x = 120, y = 80
Ans 06.
5 3
410
2 2
Z x y = + +
60 0
50 0
100 ( ) 0
60 0
, 0
x
y
x y
x y
x y
- =
- =
- + =
+ - =
=
minimum = 510
when D ? 10
E ? 50
F ? 40
Ans 07.
3
3950
10 10
x y
Z = + +
4500 0
3000 0
3500 0
7000 ( ) 0
0, 0
x
y
x y
x y
x y
- =
- =
+ - =
- + =
= =
Minimum = 4400
A
B
E F D
100
100-(x+y)
40
x+y-60
50
50-y
50
Y
60
60-x
X
A
B
E F D
Y
X
7 0 0 0 L
7000 - (x+ y)
3 5 0 0
x+ y-3500
4 0 0 0 L
3 0 0 0 -y
3 0 0 0
4500-x
4 5 0 0
Page 3

CBSE TEST PAPER-02
CLASS - XII MATHEMATICS (Linear Programming)
Ans 01.  Let the two tailors work for x days and y days respectively
Z = 150x + 200y
6x + 10y = 60
3 5 30
4 4 32
8 and x 0, y 0
x y
x y
x y
? + =
+ =
? + = = =
Z is minimum = 1350
When A work for 5 days B work for 3 days
Ans 02.  Let P = x
Q = y
Z = 250x + 200y
3x + 1.5y = 18
2.5x + 11.25y = 45
2x + 3y = 24
x =0, y = 0
Z = Rs 1950
When x = 3 y = 6
Number of bags of brand P = 3 bags of brand Q = 6
Ans 03.  Let the dietician mix x Kg of food X and y Kg of food Y.
Z = 16x + 20y
x + 2y = 10
2x + 2y =12
6
3 8
x y
x y
? + =
+ =
Cost is minimum = 112  When 2 Kg of food X and 4 Kg of food Y are mixed.
Ans 04.  Let x toys of type A and y toys of type B
15
5
2
12 6 360
2 60
18 360
Z x y
x y
x y
x
= +
+ =
? + =
=
20
6 9 360
x
x y
? =
+ =
2 3 120
0, y 0
x y
x
? + =
= =
profit is maximum = 262.5 at A = 15 B = 30
Ans 05.  X passengers travel by executive class and y passengers travel by economy class. L
Z = 1000x + 600y
x + y = 200
x = 20
y = 80
x = 0, y = 0
profit is maximum = 168000
When x = 120, y = 80
Ans 06.
5 3
410
2 2
Z x y = + +
60 0
50 0
100 ( ) 0
60 0
, 0
x
y
x y
x y
x y
- =
- =
- + =
+ - =
=
minimum = 510
when D ? 10
E ? 50
F ? 40
Ans 07.
3
3950
10 10
x y
Z = + +
4500 0
3000 0
3500 0
7000 ( ) 0
0, 0
x
y
x y
x y
x y
- =
- =
+ - =
- + =
= =
Minimum = 4400
A
B
E F D
100
100-(x+y)
40
x+y-60
50
50-y
50
Y
60
60-x
X
A
B
E F D
Y
X
7 0 0 0 L
7000 - (x+ y)
3 5 0 0
x+ y-3500
4 0 0 0 L
3 0 0 0 -y
3 0 0 0
4500-x
4 5 0 0
Ans 08.   Let the fruit grower mix x bags of brand P and Y bags of brand Q
7
3
2
Z x y = +
2 240
3
3 270
2
3
2 310
2
0, 0
x y
x y
x y
x y
+ =
+ =
+ =
= =
minimum = 470 Kg
P = 40
Q = 100
Ans 09.  Let Anil invest x in bond A and Y in bond B,
8 10
100 100
x y
P = +
x + y = 12000
x = 2000
y = 4000
x = 0, y = 0
P is maximum = 1160
x = 2000
y = 10,000
Ans 10. X dolls of type A and y dolls of type B.
Z = 12x + 16y
X + y = 1200
2
3 600
x
y
x y
=
= +
Profit is maximum = 16000
A = 800
B = 400
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