Solution- Linear Programming Test-1 Class 12 Notes | EduRev

Class 12 : Solution- Linear Programming Test-1 Class 12 Notes | EduRev

 Page 1


CBSE TEST PAPER-01 
CLASS - XII MATHEMATICS (Linear Programming) 
Topic: - Linear Programming [ANSWERS] 
Ans 01. Let food P consist of x Kg and food Q consists of Y Kg. 
Z = 60x + 80y  
3x + 4y = 8 
5x + 2y = 11  
x = 0  
y = 0 
Hence, Cost is minimum  = Rs 160 
When x = 2,   y = 
1
2
Ans 02. Let x  be number of cakes of first kind and y the number of cakes of other kind. 
Z = x + y  
200x + 100y = 5000 
? 2x + y = 50
25x + 50y = 1000 
? x + 2y = 40
x = 0, y = 0 
Maximum number of cakes 
Z = 30 
When x = 20, y = 10.  
Ans 03.  Let the number of cricket and the number of cricket bats to be made in a day be x 
and y respectively.  
Z = x + y  
and also P = 20x + 10y 
3
3 42
2
2 28
3 24
0, 0
x y
x y
x y
x y
+ =
? + =
+ =
= =
(i) Maximum Z = 16 at  x = 4  y = 12 
(ii) P = 20×4 +10×12 
= 200  
Page 2


CBSE TEST PAPER-01 
CLASS - XII MATHEMATICS (Linear Programming) 
Topic: - Linear Programming [ANSWERS] 
Ans 01. Let food P consist of x Kg and food Q consists of Y Kg. 
Z = 60x + 80y  
3x + 4y = 8 
5x + 2y = 11  
x = 0  
y = 0 
Hence, Cost is minimum  = Rs 160 
When x = 2,   y = 
1
2
Ans 02. Let x  be number of cakes of first kind and y the number of cakes of other kind. 
Z = x + y  
200x + 100y = 5000 
? 2x + y = 50
25x + 50y = 1000 
? x + 2y = 40
x = 0, y = 0 
Maximum number of cakes 
Z = 30 
When x = 20, y = 10.  
Ans 03.  Let the number of cricket and the number of cricket bats to be made in a day be x 
and y respectively.  
Z = x + y  
and also P = 20x + 10y 
3
3 42
2
2 28
3 24
0, 0
x y
x y
x y
x y
+ =
? + =
+ =
= =
(i) Maximum Z = 16 at  x = 4  y = 12 
(ii) P = 20×4 +10×12 
= 200  
Ans 04. Let the manufacture produce x nuts and y bolts 
Z = 17.50x + 7y 
x + 3y = 12 
3x + y = 12  
X 1 y = 0  
Maximum profit 
Z = Rs 73. 50 at  
X = 3, y = 3  
Ans 05.  Let the manufacturer produce x packages of screw A and y packages Screw B. 
Z = 7x +10y  
4x + 6y = 240 
2 3 120
6 3 240
x y
x y
? + =
+ =
2 80 x y ? + =
x=0,y =0   
profit is maximum = 410  
When 30 packages of screw A and 20 package 
of screw B.  
Ans 06.  Let x be pedestal lamps and y wooden shades 
Z = 5x + 3y 
2x + y = 12 
3x + 2y = 20  
x = 0, y = 0  
profit maximum  
when 4 pedestal lamps 
4 wooden shades  
Ans 07.  Let x souvenirs of type A and y souvenirs of type B 
Z = 5x + 6y 
5x + 8y = 200 
10x + 8y = 240 
? 5x + 4y = 120
x = 0, y = 0. 
Maximum profit is Rs 160  
When 8 souvenirs of Type A and 20 souvenirs 
of type B.  
Page 3


CBSE TEST PAPER-01 
CLASS - XII MATHEMATICS (Linear Programming) 
Topic: - Linear Programming [ANSWERS] 
Ans 01. Let food P consist of x Kg and food Q consists of Y Kg. 
Z = 60x + 80y  
3x + 4y = 8 
5x + 2y = 11  
x = 0  
y = 0 
Hence, Cost is minimum  = Rs 160 
When x = 2,   y = 
1
2
Ans 02. Let x  be number of cakes of first kind and y the number of cakes of other kind. 
Z = x + y  
200x + 100y = 5000 
? 2x + y = 50
25x + 50y = 1000 
? x + 2y = 40
x = 0, y = 0 
Maximum number of cakes 
Z = 30 
When x = 20, y = 10.  
Ans 03.  Let the number of cricket and the number of cricket bats to be made in a day be x 
and y respectively.  
Z = x + y  
and also P = 20x + 10y 
3
3 42
2
2 28
3 24
0, 0
x y
x y
x y
x y
+ =
? + =
+ =
= =
(i) Maximum Z = 16 at  x = 4  y = 12 
(ii) P = 20×4 +10×12 
= 200  
Ans 04. Let the manufacture produce x nuts and y bolts 
Z = 17.50x + 7y 
x + 3y = 12 
3x + y = 12  
X 1 y = 0  
Maximum profit 
Z = Rs 73. 50 at  
X = 3, y = 3  
Ans 05.  Let the manufacturer produce x packages of screw A and y packages Screw B. 
Z = 7x +10y  
4x + 6y = 240 
2 3 120
6 3 240
x y
x y
? + =
+ =
2 80 x y ? + =
x=0,y =0   
profit is maximum = 410  
When 30 packages of screw A and 20 package 
of screw B.  
Ans 06.  Let x be pedestal lamps and y wooden shades 
Z = 5x + 3y 
2x + y = 12 
3x + 2y = 20  
x = 0, y = 0  
profit maximum  
when 4 pedestal lamps 
4 wooden shades  
Ans 07.  Let x souvenirs of type A and y souvenirs of type B 
Z = 5x + 6y 
5x + 8y = 200 
10x + 8y = 240 
? 5x + 4y = 120
x = 0, y = 0. 
Maximum profit is Rs 160  
When 8 souvenirs of Type A and 20 souvenirs 
of type B.  
Ans 08.  Let the merchant stock x desktop computers and y portable computer. 
Z = 4500x + 5000y 
x + y =250 
25000x + 40000y = 700000 
? 5x + 8y = 1400
x = 0,  y = 0.  
Profit is maximum = 1150000 
When 250 desktop computers and 50 
portable computers are stocked.  
Ans 09.  Let the diet contain x unit of food F 1 and y units of food F 2. 
Z = 4x +6y 
3x + 6y = 80 
4x + 3y = 100 
X = 0, y = 0  
Z is minimum when 24 units of food F 1 and 
4
3
unit of food F 2 are mixed minimum cost =
104 .  
Ans 10.  Let the farmer use x Kg of F 1 and y Kg of F 2. 
Z = 6x + 5y 
10 5
14
100 100
6 10
14
100 100
0, 0.
x y
x y
x y
+ =
+ =
= =
 
Minimum cost 
Z = 100  
at  x = 100  
y = 80  
Read More
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Content Category

Related Searches

practice quizzes

,

Extra Questions

,

Semester Notes

,

Summary

,

Free

,

pdf

,

Previous Year Questions with Solutions

,

mock tests for examination

,

past year papers

,

Solution- Linear Programming Test-1 Class 12 Notes | EduRev

,

Solution- Linear Programming Test-1 Class 12 Notes | EduRev

,

ppt

,

MCQs

,

Viva Questions

,

Objective type Questions

,

Sample Paper

,

video lectures

,

Exam

,

study material

,

Solution- Linear Programming Test-1 Class 12 Notes | EduRev

,

Important questions

,

shortcuts and tricks

;