Linear Programming Test

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Linear Programming Test - 2

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Weekly Quiz Competition

Question 1
4 / -1

Which of the following sets are not convex?

A
{(x , y) : 8x² + 6y² ≤ 24}

B
{(x , y) : 6 ≤ x² + y² ≤ 36}

C
{(x , y): y ≥ 3, y ≥ 30}

D
{(x , y): x² ≤ y
Question 2
4 / -1

Consider the linear programming problem
Maximise z = 4x + y
Subject to constraints x + y ≤ 50, x + y ≥ 100,
and x, y ≥ 0
Then, maximum value of z is

A
0

B
50

C
100

D
does not exist
Question 3
4 / -1

The point which provides the solution of the linear programming problem, maximise z = 45x + 55y
Subject to constraints x, y ≥ 0, 6x + 4y ≤ 120 and 3x + 10y ≤ 180 is

A
( 15 , 10 )

B
( 10 , 15 )

C
( 0 , 18 )

D
( 20 , 0 )
Question 4
4 / -1

The linear programming problem
Maximise z = x₁ + x₂
Subject to constraints x₁ + 2x₂ ≤ 2000, x₁ + x₂ ≤ 1500, x₂ ≤ 600 and x₁ ≥ 0 has

A
no feasible solution

B
unique optimal solution

C
a finite number of optimal solutions

D
infinite number of optimal solutions
Question 5
4 / -1

The optimal value of the objective function is attained at the point is

A
given by intersection of inequations with axes only

B
given by intersection of inequations with X-axis only

C
given by corner points of the feasible region

D
None of the above
Question 6
4 / -1

The maximum value of z = 9x + 13y, subject to constraints 2x + 3y ≤ 18, 2x + y ≤ 10, x ≥ 0 and y ≥ 0 is

A
130

B
81

C
79

D
99
Question 7
4 / -1

The maximum value of z = 10x + 6y, subject to constraints x ≥ 0, y ≥ 0, x + y ≤ 12, 2x + y ≤ 20 is

A
72

B
80

C
104

D
110
Question 8
4 / -1

A vertex of a feasible region by the linear constraints 3x + 4y ≤ 18, 2x + 3y ≥ 3 and x, y ≥ 0 is

A
(0, 2)

B
(4.8, 0)

C
(0, 3)

D
None of these
Question 9
4 / -1

For an LPP, minimise z = 2x + y subject to constraints 5x + 10y ≤ 50 , x + y ≥ 1, y ≤ 4 and x,y ≥ 0, then z is equal to

A
0

B
1

C
2

D
12
Question 10
4 / -1

For the LPP, minimise z = x₁ + x₂ such that inequalities 5x₁ + 10x₂ ≥ 0, x₁ + x₂ ≤ 1, x₂ ≤ 4 and x₁ , x₂ ≥ 0

A
There is a bounded solution

B
There is no solution

C
There are infinite solutions

D
None of the above

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Linear Programming Test - 2

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Question 1

{(x , y) : 8x2 + 6y2 ≤ 24}

{(x , y) : 6 ≤ x2 + y2 ≤ 36}

{(x , y): y ≥ 3, y ≥ 30}

{(x , y): x2 ≤ y

Question 2

0

50

100

does not exist

Question 3

( 15 , 10 )

( 10 , 15 )

( 0 , 18 )

( 20 , 0 )

Question 4

no feasible solution

unique optimal solution

a finite number of optimal solutions

infinite number of optimal solutions

Question 5

given by intersection of inequations with axes only

given by intersection of inequations with X-axis only

given by corner points of the feasible region

None of the above

Question 6

130

81

79

99

Question 7

72

80

104

110

Question 8

(0, 2)

(4.8, 0)

(0, 3)

None of these

Question 9

0

1

2

12

Question 10

There is a bounded solution

There is no solution

There are infinite solutions

None of the above

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{(x , y) : 8x² + 6y² ≤ 24}

{(x , y) : 6 ≤ x² + y² ≤ 36}

{(x , y): x² ≤ y