Mathematics Test

Question 1
5 / -1

In linear programming problem, the term which is not involved is

A
Objective function

B
Linear scale

C
Linear constraints

D
Decision variables

Question 2
5 / -1

A feasible solution to the linear programming problem should

A
Satisfy the problem constraint

B
Optimize the objective function

C
Satisfy the problem constraints and non-negatively restrictions

D
None of the above

Question 3
5 / -1

There are two linear inequations represented by x - y ≥ 0 and x + y < 5. The lines are being drawn in the figure below and some of the regions are being shaded by different colours.

Which region based on colour contains the solutions of these two inequations?

A
Green

B
Yellow

C
Black

D
Red

Question 4
5 / -1

In a graphical solution of solving Linear Programming problem to convert inequalities into equations, it is essential to use-

A
Them to be slack variables

B
Them to be artificial surplus variables and slack variables both

C
Them to be equations

D
Them to be artificial surplus variables

Question 5
5 / -1

Consider the linear programming problem for the profit maximization (Rs) of a manufacturer with the objective function as,
Zmax = 2000x + 3000y subjected to
3x + 2y ≤ 90,
x + 2y ≤ 100, x ≥ 0, y ≥ 0
The manufacturer can make a maximum profit of Rs?

A
1,50,000 Rs

B
1,35,000 Rs

C
60,000 Rs

D
Infeasible solution

Question 6
5 / -1

Consider the following Linear Programming Problem,
Maximize Z = 7x + 3y,
Subject to constraints
x + 3y ≤ 5
x + y ≤ 4
x, y ≥ 0
Number of solutions for the LP will be

A
Infinite solutions

B
Unique Solution

C
No Solution

D
Two Solutions

Question 7
5 / -1

A housewife 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 1 kg of food is given below:

Vitamin A
Vitamin B
Vitamin C
Food X
1
2
3
Food Y
2
2
1
Given that 1 kg of food X costs Rs. 6 and 1 kg of food Y costs Rs. 10. Which of the following is representing the objective function subject to the constraints.

A
Z = 6x + 10y subjected to
x + 2y ≥ 10,
2x + 2y = 12,
3x + y = 8,
x , y ≥ 0

B
Z = 6x + 10y subjected to
x + 2y ≥ 10,
2x + 2y ≥ 12,
3x + y ≥ 8,
x , y ≥ 0

C
min Z = 6x + 10y subjected to
x + 2y ≥ 10,
2x + 2y ≥ 12,
3x + y ≥ 8,
x , y ≥ 0

D
min Z = 6x + 10y subjected to
x + 2y ≥ 10,
2x + 2y = 12,
3x + y = 8,
x , y ≥ 0

Question 8
5 / -1

Consider the following linear programming problem:
Maximize z = 6x + 10y
Subject to x ≤ 4
y ≤ 6
3x + 2y ≤ 18
x ≥ 0, y ≥ 0
What is the number of points that will be representing the corner points of the feasible region?

A
3

B
5

C
4

D
None

Question 9
5 / -1

For the Linear Programming Problem,

Max Z = 7x + 3y, subject to constraints

x + 3y ≥ 5

x + y ≥ 2

x, y ≥ 0

Then this Linear programming problem is having?

A
Feasible and bounded region 3 corner points

B
Infeasible region

C
Feasible but unbounded region with 3 corner points

D
Feasible but unbounded region with 2 corner points

Question 10
5 / -1

The number of solutions in a linear programming model to maximize the objective function 7x + y subject to the constraints,

x - y ≥ 2,

x - y ≤ - 3,

x, y ≥ 0 will be,

A
More than two solutions

B
Exactly two solutions

C
No solution

D
A unique solution

Submit Test

	Vitamin A	Vitamin B	Vitamin C
Food X	1	2	3
Food Y	2	2	1

Mathematics Tes...

Question 1

Objective function

Linear scale

Linear constraints

Decision variables

Question 2

Satisfy the problem constraint

Optimize the objective function

Satisfy the problem constraints and non-negatively restrictions

None of the above

Question 3

Green

Yellow

Black

Red

Question 4

Them to be slack variables

Them to be artificial surplus variables and slack variables both

Them to be equations

Them to be artificial surplus variables

Question 5

1,50,000 Rs

1,35,000 Rs

60,000 Rs

Infeasible solution

Question 6

Infinite solutions

Unique Solution

No Solution

Two Solutions

Question 7

Z = 6x + 10y subjected to x + 2y ≥ 10, 2x + 2y = 12, 3x + y = 8, x , y ≥ 0

Z = 6x + 10y subjected to x + 2y ≥ 10, 2x + 2y ≥ 12, 3x + y ≥ 8, x , y ≥ 0

min Z = 6x + 10y subjected to x + 2y ≥ 10,2x + 2y ≥ 12,3x + y ≥ 8,x , y ≥ 0

min Z = 6x + 10y subjected to x + 2y ≥ 10, 2x + 2y = 12, 3x + y = 8, x , y ≥ 0

Question 8

3

5

4

None

Question 9

Feasible and bounded region 3 corner points

Infeasible region

Feasible but unbounded region with 3 corner points

Feasible but unbounded region with 2 corner points

Question 10

More than two solutions

Exactly two solutions

No solution

A unique solution

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Z = 6x + 10y subjected to
x + 2y ≥ 10,
2x + 2y = 12,
3x + y = 8,
x , y ≥ 0

Z = 6x + 10y subjected to
x + 2y ≥ 10,
2x + 2y ≥ 12,
3x + y ≥ 8,
x , y ≥ 0

min Z = 6x + 10y subjected to
x + 2y ≥ 10,
2x + 2y ≥ 12,
3x + y ≥ 8,
x , y ≥ 0

min Z = 6x + 10y subjected to
x + 2y ≥ 10,
2x + 2y = 12,
3x + y = 8,
x , y ≥ 0