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) 
Topic: - Linear Programming [ANSWERS] 
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) 
Topic: - Linear Programming [ANSWERS] 
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) 
Topic: - Linear Programming [ANSWERS] 
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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