Infinite number of optimal solutions

A finite number of optimal solutions

JEE Questions for Maths Miscellaneous Quiz 16

Mohan wants to invest the total amount of Rs. 15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least Rs. 2000 in saving certificates and Rs. 2500 in national saving bonds. The interest rate is 8% on saving certificate and 10% on national saving bonds per annum. He invest x in saving certificates and y in national saving bonds. Then the objective function for this problem is

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0%
2)
0%
0%

A film produces two types of products A and B. The profit on both is 2 per item. Every product requires processing on machines M₁ and M₂. For A, machines M₁ and M₂ takes 1 minute and 2 minute respectively and for B, machines M₁ and M₂ takes the rime 1 minute each. The machines M₁, M₂ are not available more

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0%
2)
0%
0%

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0%
2)
0%
0%

The objective function in the above question is

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2x + y
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x + 2y
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2x + 2y
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8x + by

The objective function for the above question is

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10x + 14y
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5x + 10y
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3x + 5y
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5y + 3x

The vertices of a feasible region of the above question are

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(0, 18), (36, 0)
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(0, 18), (10,
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(10, 13), (8,
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(10, 13), (8, 14), (12,

The maximum value of objective function in the above question is

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100
0%
92
0%
95
0%
94

A factory produces two products A and B. In the manufacturing of product A, the machine and the carpenter requires 3 hour each and in manufacturing of product B, the machine and carpenter requires 5 hour and 3 hour respectively The machine and carpenter work at most 80 hour and 50 hour per week respectively. The profit on A and B is Rs. 6 and 8 respectively. If profit is maximum by manufacturing x and y units of A and B type product respectively, then for the function 6x + 8y the constraints are

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0%
2)
0%
0%

A shopkeeper wants to purchase two articles A and B of cost price Rs. 4 and 3 respectively. He thought that he may earn 30 paise by selling article A and 10 paise by selling article B. He has not to purchase total article worth more than Rs. 24. If he purchases the number of articles of A and B, x and y respectively, then linear constraints are

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0%
2)
0%
0%

In the above question the iso-profit line is

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3x + y = 30
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x + 3y = 20
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3x – y = 20
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4x + 3y = 24

The sum of two positive integers is at most 5. The difference between two times of second number and first number is at most 4. If the first number is x and second number y, then for maximizing the product of these two numbers, the mathematical formulation is

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0%
2)
0%
0%
None of these

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12
0%
24
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36
0%
40

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2
0%
8
0%
10
0%
12

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There is a bounded solution
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There is no solution
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There are infinite solutions
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None of the above

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15
0%
36
0%
60
0%
40

A linear programming of linear functions deals with

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Minimizing
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Optimizing
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Maximizing
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None of these

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-10
0%
-20
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0
0%
10

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(0, 0)
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(1.5, 1.
0%
(2,
0%
(0,

The minimum value of objective function c = 2x + 2y in the given feasible region, is

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134
0%
40
0%
38
0%
80

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10
0%
12
0%
6
0%
5

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x = 0, y = 0, z = 0
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x = 3, y =3, z = 6
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There are infinitely solutions
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None of the above

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0%
2)
0%
0%

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x = 12,y = 18
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x = 18, y = 12
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x = 12,y = 12
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x = 20, y = 10

An industry produces two types of models M₁, M₂. Each M₁ model needs 4 hours for grinding and 2 hours for polishing, whereas each M₂ model needs 2 hours for grinding and 5 hours for polishing. There are 2 grinders and 3 polishers in the industry. Each grinder can work for 40 hours a week whilc each polisher can work for 60 hours a week. Each M₁ model earns a profit of 3 and each M₂ model earns 4 profit. To ensure the maximum profit the production capacity allocated to two types of models in a week is