Mathematics Test

Question 1
5 / -1

What is the interpretation of the shaded region in a Linear Programming Problems?

A
It is very important area

B
It will not satisfy the limitations

C
It will satisfy few constraints

D
It will satisfy all constraints

Question 2
5 / -1

In the problem Z = 3x₁ + 2x₂
Subject to 2x₁ + x₂ ≤ 20         ---(i)
x₁ ≤ 10        ---(ii)
x₁, x₂ ≥ 0     ---(iii)
constraint (iii) is known as

A
availability constraint

B
non-negativity constraint

C
object constraint

D
none of these

Question 3
5 / -1

Simplex method of solving linear programming problem uses

A
all the points in the feasible region

B
only the corner points of the feasible region

C
intermediate points within the infeasible region

D
only the interior points in the feasible region

Question 4
5 / -1

Consider the following LPP:
Maximize z = 60X₁ + 50X₂
Subject to X₁ + 2X₂ ≤ 40,
3X₁ + 2X₂ ≤ 60
where, X₁ and X₂ ≥ 0

A
The LPP has a unique optimal solution

B
The LPP is infeasible

C
The LPP is unbound

D
The LPP has multiple optimal solutions

Question 5
5 / -1

While solving a linear programming model, if a redundant constraint is added, then what will be its effect on existing solution?

A
There will be no effect

B
The solution space will get further constrained

C
The solution space becomes concave

D
The problem no longer remains solvable

Question 6
5 / -1

Consider the following Linear Programming Problem (LPP).
Maximise Z = x₁ + 2x₂
Subject to:
x₁ ≤ 2
x₂ ≤ 2
x₁ + x₂ ≤ 2
x₁, x₂ ≥ 0 (i.e. +ve decision variables)
What is the optimal solution to the above LPP?

A
2, 2

B
0, 2

C
2, 0

D
0, 0

Question 7
5 / -1

A manufacturing unit produces two products Pl and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit earned. The maximum quantity available per day for M1, M2 and M3 is also provided. Then which of the following mathematical formulation is correct for this L.P.P.?

M1
M2
M3
Profit per piece (Rs.)
P1 ( x1)
2
2
0
150
P2 (x2.)
3
1
2
100
Maximum quantity available per day
70
50
40

Where the number of the products of P! and P2 types are x1  and x2.

A
Max Z = 100x1 + 150x2 subjected to
2x1 + 3x2 ≤ 70,
2x1 + x2 ≤ 50,
2x2 ≤ 40,
x1  ≥ 0 and x2. ≥ 0

B
Max Z = 150x1 + 100x2 subjected to
2x1 + 3x2 ≤ 70,
2x1 + x2 ≤ 50,
2x2 ≤ 40,
x1  ≥ 0 and x2. ≥ 0

C
Both can be true

D
None of the above

Question 8
5 / -1

Max z = x₁ + x₂ subject to constraints:
x₁ + x₂ ≤ 1
-3x₁ + x₂ ≥ 3
x₁, x₂ ≥ 0
For the above LPP, the solution is

A
Unique solution

B
Unbounded solution

C
Infeasible solution

D
Cannot be predicted

Question 9
5 / -1

Consider the following Linear Programming Problem (LPP):
Maximize Z = 3x₁ + 2x₂ Subject to
x₁ ≤ 4
x₂ ≤ 6
3x₁ + 2x₂ ≤ 18
x₁ ≥ 0, x₂ ≥ 0

A
The LPP has a unique optimal solution

B
The LPP is infeasible

C
The LPP is unbounded

D
The LPP has multiple optimal solutions

Question 10
5 / -1

An objective function is given by
Z(x₁, x₂) = 3x₁ + 9x₂
The constraints are:
x₁ + x₂ ≤ 8; x₁ + 2x₂ ≤ 4; x₁ ≥ 0; x₂ ≥ 0
What will be the maximum value of the objective function?

A
12

B
zero

C
24

D
18

Submit Test

	M1	M2	M3	Profit per piece (Rs.)
P1 ( x1)	2	2	0	150
P2 (x2.)	3	1	2	100
Maximum quantity available per day	70	50	40

Mathematics Tes...

Question 1

It is very important area

It will not satisfy the limitations

It will satisfy few constraints

It will satisfy all constraints

Question 2

availability constraint

non-negativity constraint

object constraint

none of these

Question 3

all the points in the feasible region

only the corner points of the feasible region

intermediate points within the infeasible region

only the interior points in the feasible region

Question 4

The LPP has a unique optimal solution

The LPP is infeasible

The LPP is unbound

The LPP has multiple optimal solutions

Question 5

There will be no effect

The solution space will get further constrained

The solution space becomes concave

The problem no longer remains solvable

Question 6

2, 2

0, 2

2, 0

0, 0

Question 7

Max Z = 100x1 + 150x2 subjected to2x1 + 3x2 ≤ 70,2x1 + x2 ≤ 50,2x2 ≤ 40, x1 ≥ 0 and x2. ≥ 0

Max Z = 150x1 + 100x2 subjected to 2x1 + 3x2 ≤ 70, 2x1 + x2 ≤ 50, 2x2 ≤ 40, x1 ≥ 0 and x2. ≥ 0

Both can be true

None of the above

Question 8

Unique solution

Unbounded solution

Infeasible solution

Cannot be predicted

Question 9

The LPP has a unique optimal solution

The LPP is infeasible

The LPP is unbounded

The LPP has multiple optimal solutions

Question 10

12

zero

24

18

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Question Analysis

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Max Z = 100x1 + 150x2 subjected to
2x1 + 3x2 ≤ 70,
2x1 + x2 ≤ 50,
2x2 ≤ 40,
x1 ≥ 0 and x2. ≥ 0

Max Z = 150x1 + 100x2 subjected to
2x1 + 3x2 ≤ 70,
2x1 + x2 ≤ 50,
2x2 ≤ 40,
x1 ≥ 0 and x2. ≥ 0