Linear Programming Test

Question 1
1 / -0

The objective function $$z = 4x_{1} + 5x_{2}$$, subject to $$2x_{1} + x_{2}\geq 7, 2x_{1} + 3x_{2} \leq 15, x_{2}\leq 3, x_{1}, x_{2} \geq 0$$ has minimum value at the point.

A
On x-axis

B
On y-axis

C
At the origin

D
On the parallel to x-axis

Question 2
1 / -0

The objective function of LPP defined over the convex set attains its optimum value at

A
atleast two of the corner points

B
all the corner points

C
atleast one of the corner points

D
none of the corner points

Question 3
1 / -0

The constraints
$$-{ x }_{ 1 }+{ x }_{ 2 }\le 1$$
$$-{ x }_{ 1 }+3{ x }_{ 2 }\le 9$$
$${x}_{1},{x}_{2}\ge 0$$ defines on

A
Bounded feasible space

B
Unbounded feasible space

C
Both bounded and unbounded feasible

D
None of the above

Question 4
1 / -0

An article manufactured by a company consists of two parts $$X$$ and $$Y$$. In the process of manufacture of the part $$X$$. $$9$$ out of $$100$$ parts may be defective. Similarly $$5$$ out of $$100$$ are likely to be defective in part $$Y$$. Calculate the probability that the assembled product will not be defective.

A
$$0.86$$

B
$$0.864$$

C
$$0.8456$$

D
$$0.8645$$

Question 5
1 / -0

The corner points of the feasible region determined by the system of linear constraints are $$(0, 10), (5, 5), (15, 15), (0, 20)$$. Let $$z=px+qy$$ where $$p, q > 0$$. Condition on p and q so that the maximum of z occurs at both the points $$(15, 15)$$ and $$(0, 20)$$ is __________.

A
$$q=2p$$

B
$$p=2p$$

C
$$p=q$$

D
$$q=3p$$

Question 6
1 / -0

Corner points of the bounded feasible region for an LP problem are $$A(0,5) B(0,3) C(1,0) D(6,0)$$. Let $$z = -50x + 20y$$ be the objective function. Minimum value of z occurs at ______ center point.

A
$$(0,5)$$

B
$$(1,0)$$

C
$$(6,0)$$

D
$$(0,3)$$

Question 7
1 / -0

The corner points of the feasible region are $$A(0,0),B(16,0),C(8,16)$$ and $$D(0,24)$$. The minimum value of the objective function $$z=300x+190y$$ is _______

A
$$5440$$

B
$$4800$$

C
$$4560$$

D
$$0$$

Question 8
1 / -0

The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.

Colour Number of cars manufactured
Vento Creta WagonR
Red 65 88 93
White 54 42 80
Black 66 52 88
Sliver 37 49 74
Which car was twice the number of silver Vento?

A
Silver WagonR

B
Red WagonR

C
Red Vento

D
White Creta

Question 9
1 / -0

A firm manufactures three products $$A,B$$ and $$C$$. Time to manufacture product $$A$$ is twice that for $$B$$ and thrice that for $$C$$ and if the entire labour is engaged in making product $$A,1600$$ units of this product can be produced.These products are to be produced in the ratio $$3:4:5.$$ There is demand for at least $$300,250$$ and $$200$$ units of products $$A,B$$ and $$C$$ and the profit earned per unit is Rs.$$90,$$ Rs$$40$$ and Rs.$$30$$ respectively.
Raw
material Requirement per unit product(Kg)
A Requirement per unit product(Kg)
B Requirement per unit product(Kg)
C Total availability (kg)
$$P$$ $$6$$ $$5$$ $$2$$ $$5,000$$
$$Q$$ $$4$$ $$7$$ $$3$$ $$6,000$$
Formulate the problem as a linear programming problem and find all the constraints for the above product mix problem.

A
$$3{x}_{1}-4{x}_{2}=0$$ and $$5{x}_{2}-4{x}_{3}=0$$ where $${x}_{1},{x}_{2},{x}_{3}\ge0$$

B
$$4{x}_{1}-3{x}_{2}=0$$ and $$5{x}_{2}-4{x}_{3}=0$$ where $${x}_{1},{x}_{2},{x}_{3}\ge0$$

C
$$4{x}_{1}-3{x}_{2}=0$$ and $$4{x}_{2}-5{x}_{3}=0$$ where $${x}_{1},{x}_{2},{x}_{3}\ge0$$

D
$$4{x}_{1}-3{x}_{2}=0$$ and $$5{x}_{2}-4{x}_{3}=0$$ where $${x}_{1},{x}_{2},{x}_{3}\le0$$

Question 10
1 / -0

Equation of normal drawn to the graph of the function defined as $$f(x)=\dfrac{\sin x^2}{x}$$, $$x\neq 0$$ and $$f(0)=0$$ at the origin is?

A
$$x+y=0$$

B
$$x-y=0$$

C
$$y=0$$

D
$$x=0$$

Submit Test

Colour	Number of cars manufactured
Colour	Vento	Creta	WagonR
Red	65	88	93
White	54	42	80
Black	66	52	88
Sliver	37	49	74

Raw material	Requirement per unit product(Kg) A	Requirement per unit product(Kg) B	Requirement per unit product(Kg) C	Total availability (kg)
$$P$$	$$6$$	$$5$$	$$2$$	$$5,000$$
$$Q$$	$$4$$	$$7$$	$$3$$	$$6,000$$

Linear Programm...

Question 1

On x-axis

On y-axis

At the origin

On the parallel to x-axis

Question 2

atleast two of the corner points

all the corner points

atleast one of the corner points

none of the corner points

Question 3

Bounded feasible space

Unbounded feasible space

Both bounded and unbounded feasible

None of the above

Question 4

$$0.86$$

$$0.864$$

$$0.8456$$

$$0.8645$$

Question 5

$$q=2p$$

$$p=2p$$

$$p=q$$

$$q=3p$$

Question 6

$$(0,5)$$

$$(1,0)$$

$$(6,0)$$

$$(0,3)$$

Question 7

$$5440$$

$$4800$$

$$4560$$

$$0$$

Question 8

Silver WagonR

Red WagonR

Red Vento

White Creta

Question 9

$$3{x}_{1}-4{x}_{2}=0$$ and $$5{x}_{2}-4{x}_{3}=0$$ where $${x}_{1},{x}_{2},{x}_{3}\ge0$$

$$4{x}_{1}-3{x}_{2}=0$$ and $$5{x}_{2}-4{x}_{3}=0$$ where $${x}_{1},{x}_{2},{x}_{3}\ge0$$

$$4{x}_{1}-3{x}_{2}=0$$ and $$4{x}_{2}-5{x}_{3}=0$$ where $${x}_{1},{x}_{2},{x}_{3}\ge0$$

$$4{x}_{1}-3{x}_{2}=0$$ and $$5{x}_{2}-4{x}_{3}=0$$ where $${x}_{1},{x}_{2},{x}_{3}\le0$$

Question 10

$$x+y=0$$

$$x-y=0$$

$$y=0$$

$$x=0$$

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