Linear Programming Test

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Linear Programming Test - 6

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Weekly Quiz Competition

Question 1
1 / -0.25

If the system of constraints has no point which satisfies all the constraints and non-negativity restrictions then the solution of a LPP is an

A
Infeasible solution

B
Feasible solution

C
Optimal solution

D
None of these
Question 2
1 / -0.25

The optimum value of the objective function is attained at the points

A
Corner points of feasible region

B
Any point of the feasible region

C
On x-axis

D
On y-axis

Solution

The optimal value of the objective function is attained at the points given by corner points of the feasible region.
Question 3
1 / -0.25

The maximum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≤160, 5x + 2y ≤200, x + 2y ≤80 ;
x, y ≥0 attains at

A
x = 40, y = 0

B
x = 40, y = 25

C
x = 0, y = 25

D
x = 30. y = 25
Question 4
1 / -0.25

A feasible solution of a LPP if it also optimizes the objective function is called

A
Optimal feasible solution

B
Optimal solution

C
Feasible solution

D
None of these
Question 5
1 / -0.25

Shape of the feasible region formed by the following constraints is x + y ≤10, x + y ≥6, x ≥0, y ≥0

A
Triangular

B
Unbounded

C
Trapezium

D
Pentagon

Solution

x + y ≤10
x + y = 10
For x = 0, y = 10
x + y ≥6, x + y = 6
For x = 0, y =6
Hence, the image will be the trapezium.
Question 6
1 / -0.25

Region represented by x ≥0, y ≥0 is

A
Third Quadrant

B
Fourth Quadrant

C
First Quadrant

D
Second Quadrant
Question 7
1 / -0.25

Find the maximum value of z = 3x + 4y subject to constraints x + y ≤4 , x ≥0 and y ≥0

A
12

B
16

C
7

D
14
Question 8
1 / -0.25

Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is

A
At least 1

B
An infinite number

C
Zero

D
At least 2
Question 9
1 / -0.25

The set of all feasible solutions of a LPP is a ____ set.

A
Concave

B
Convex

C
Feasible

D
None of these

Solution

The set of feasible solutions to an LP (feasible region) forms a (possibly unbounded) convex set.
Question 10
1 / -0.25

Which of the following sets are convex ?

A
{(x, y) : x² + y² ≥1}

B
{(x,y) : y ≥2 , y ≤4}

C
{(x, y) : 3x² + 4y² ≥5}

D
{(x, y) : y² ≥x}

Solution

{(x,y) : y ≥2 , y ≤4} is the region between two parallel lines, so any line segment joining any two points in it lies in it. Hence, it is the convex set.

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Re-Attempt Weekly Quiz Competition

Linear Programming Test - 6

Result

Linear Programming Test - 6

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Question 1

Infeasible solution

Feasible solution

Optimal solution

None of these

Question 2

Corner points of feasible region

Any point of the feasible region

On x-axis

On y-axis

Solution

Question 3

x = 40, y = 0

x = 40, y = 25

x = 0, y = 25

x = 30. y = 25

Question 4

Optimal feasible solution ﻿

Optimal solution ﻿

Feasible solution ﻿

None of these

Question 5

Triangular

Unbounded

Trapezium

Pentagon

Solution

Question 6

Third Quadrant

Fourth Quadrant

First Quadrant

Second Quadrant

Question 7

12

16

7

14

Question 8

At least 1

An infinite number

Zero

At least 2

Question 9

Concave

Convex

Feasible

None of these

Solution

Question 10

{(x, y) : x2 + y2 ≥1}

{(x,y) : y ≥2 , y ≤4}

{(x, y) : 3x2 + 4y2 ≥5}

{(x, y) : y2 ≥x}

Solution

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Optimal feasible solution

Optimal solution

Feasible solution

{(x, y) : x² + y² ≥1}

{(x, y) : 3x² + 4y² ≥5}

{(x, y) : y² ≥x}