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# Linear Programming Test-2 (Mathematics, Class 12, CBSE) Class 12 Notes | EduRev

## Class 12 : Linear Programming Test-2 (Mathematics, Class 12, CBSE) Class 12 Notes | EduRev

Page 1

CBSE TEST PAPER-02
CLASS - XII MATHEMATICS (Linear Programming)
Topic: - Linear Programming
1. Two tailors A and B earn Rs 150 and Rs 200 per day respectively. A can stitch 6
shirts and 4 pants per day while B can stich 10 shirts and 4 Pants per day. How many
days each work if it is desired to produce at least 60 shirts and 32 pants at a
minimum labour cast?
[6]
2. A farmer mixes two brands p and Q of cattle feed. Brand P, costing Rs 250 per bag,
contains 3 units of nutritional elements A, 2.5 units of element B and 2 units of element
C. Brand Q costing Rs 200 per bag contains 1.5 units of nutritional element A, 11.25 units
of element B and 3 units of element C. The minimum requirements of nutrients A, B and
C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each
brand which should be mixed in order to produce a mixture having a minimum cost per
bag? What is the minimum cost of the mixture per bag?
[6]
3. A dietician wishes to mix together two kinds of food X and Y in such a way that the
mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of
vitamin C. The vitamin contents of one kg food are given below:
Food Vitamin A Vitamin B Vitamin C
X 1 2 3
Y 2 2 1
[6]
4. A manufacture makes tow types of toys A and B. three machines are needs for this
purpose and the time (in minutes) required for each toy on the machines is given below:
Types of Toys
Machines
I II III
A 12 18 6
B 6 0 9
Each machine is available for a maximum of 6 hours per day. If the profit on each toy on
of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys f type A and
30 of type A and 30 of type B should be manufacture in a day to get maximum.
[6]
Page 2

CBSE TEST PAPER-02
CLASS - XII MATHEMATICS (Linear Programming)
Topic: - Linear Programming
1. Two tailors A and B earn Rs 150 and Rs 200 per day respectively. A can stitch 6
shirts and 4 pants per day while B can stich 10 shirts and 4 Pants per day. How many
days each work if it is desired to produce at least 60 shirts and 32 pants at a
minimum labour cast?
[6]
2. A farmer mixes two brands p and Q of cattle feed. Brand P, costing Rs 250 per bag,
contains 3 units of nutritional elements A, 2.5 units of element B and 2 units of element
C. Brand Q costing Rs 200 per bag contains 1.5 units of nutritional element A, 11.25 units
of element B and 3 units of element C. The minimum requirements of nutrients A, B and
C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each
brand which should be mixed in order to produce a mixture having a minimum cost per
bag? What is the minimum cost of the mixture per bag?
[6]
3. A dietician wishes to mix together two kinds of food X and Y in such a way that the
mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of
vitamin C. The vitamin contents of one kg food are given below:
Food Vitamin A Vitamin B Vitamin C
X 1 2 3
Y 2 2 1
[6]
4. A manufacture makes tow types of toys A and B. three machines are needs for this
purpose and the time (in minutes) required for each toy on the machines is given below:
Types of Toys
Machines
I II III
A 12 18 6
B 6 0 9
Each machine is available for a maximum of 6 hours per day. If the profit on each toy on
of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys f type A and
30 of type A and 30 of type B should be manufacture in a day to get maximum.
[6]
5. An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on
each executive class ticket and a profit of Rs 600 is made on each economy class ticket.
The airline reserves at least 20 seats for executive class. However, at least 4 times as
many passengers prefer to travel by economy class than by the executive class. Determine
how many tickets of each type must be sold in order to maximise the profit for the airline.
What is the maximum profit?
[6]
6. Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively.
They supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals
respectively. The cost of transportation per quintal from the godowns to the shops are
given in the following table:
How should be the supplies be transported in order that the transportation cost is minimum?
What is the minimum cost?
Transportation cost per quintal (in Rs)
From/To A B
D
E
F
6
3
2.50
4
2
3
[6]
7.
An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively.
The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L,
3000L and 3500L respectively. The distances (in km) between the depots and the petrol pumps
is given in the following table:
Assuming that the transportation cost of 10 litres of oil Rs 1 per km, how should the delivery be
scheduled in order that the transportation cost is minimum? What is the minimum cost?
Transportation cost per quintal (in Rs)
From/To A B
D
E
F
6
3
2.50
4
2
3
[6]
Page 3

CBSE TEST PAPER-02
CLASS - XII MATHEMATICS (Linear Programming)
Topic: - Linear Programming
1. Two tailors A and B earn Rs 150 and Rs 200 per day respectively. A can stitch 6
shirts and 4 pants per day while B can stich 10 shirts and 4 Pants per day. How many
days each work if it is desired to produce at least 60 shirts and 32 pants at a
minimum labour cast?
[6]
2. A farmer mixes two brands p and Q of cattle feed. Brand P, costing Rs 250 per bag,
contains 3 units of nutritional elements A, 2.5 units of element B and 2 units of element
C. Brand Q costing Rs 200 per bag contains 1.5 units of nutritional element A, 11.25 units
of element B and 3 units of element C. The minimum requirements of nutrients A, B and
C are 18 units, 45 units and 24 units respectively. Determine the number of bags of each
brand which should be mixed in order to produce a mixture having a minimum cost per
bag? What is the minimum cost of the mixture per bag?
[6]
3. A dietician wishes to mix together two kinds of food X and Y in such a way that the
mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of
vitamin C. The vitamin contents of one kg food are given below:
Food Vitamin A Vitamin B Vitamin C
X 1 2 3
Y 2 2 1
[6]
4. A manufacture makes tow types of toys A and B. three machines are needs for this
purpose and the time (in minutes) required for each toy on the machines is given below:
Types of Toys
Machines
I II III
A 12 18 6
B 6 0 9
Each machine is available for a maximum of 6 hours per day. If the profit on each toy on
of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys f type A and
30 of type A and 30 of type B should be manufacture in a day to get maximum.
[6]
5. An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on
each executive class ticket and a profit of Rs 600 is made on each economy class ticket.
The airline reserves at least 20 seats for executive class. However, at least 4 times as
many passengers prefer to travel by economy class than by the executive class. Determine
how many tickets of each type must be sold in order to maximise the profit for the airline.
What is the maximum profit?
[6]
6. Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively.
They supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals
respectively. The cost of transportation per quintal from the godowns to the shops are
given in the following table:
How should be the supplies be transported in order that the transportation cost is minimum?
What is the minimum cost?
Transportation cost per quintal (in Rs)
From/To A B
D
E
F
6
3
2.50
4
2
3
[6]
7.
An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively.
The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L,
3000L and 3500L respectively. The distances (in km) between the depots and the petrol pumps
is given in the following table:
Assuming that the transportation cost of 10 litres of oil Rs 1 per km, how should the delivery be
scheduled in order that the transportation cost is minimum? What is the minimum cost?
Transportation cost per quintal (in Rs)
From/To A B
D
E
F
6
3
2.50
4
2
3
[6]
8.
A fruit grower can use two types of fertilizer in his garden, brand P and Q. The amounts (in kg)
of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brad are given in the table.
Testes indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of
potash and at most 310 kg of chlorine.
If the grower wants to minimize the amount of nitrogen added to the garden, how many bags of
each brand should be used? What is the minimum amount of nitrogen added in the garden?
Kg per bag
Brand P Brand Q
Nitrogen
Phosphoric acid
Potash
Chlorine
3
1
3
1.5
3.5
2
1.5
2
[6]
9. Anil wants to invest at most Rs 12,000 in bonds A and B. According to the rules he
has to invest at least Rs 2000 in bond A and at least Rs 4000 in bond B. If the rate of
interest on bond A is 8% per annum and on bond B, it is 10% per annum, how should
be invest the money for maximum interest.
[6]
10. A toy company manufactures two types of dolls. A and B market tests and available resources
have indicated that the combined production level should not exceed 1200 dolls per week and
the demand for dolls of type B is at most half of that for dolls of type A. Further, the
production level of dolls of type A can exceed three times the production of dolls of other type
by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on
dolls A and B, how many of each should be produced weekly in order to maximise the profit?
[6]
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