Linear Programming Test

Result

Linear Programming Test - 16

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0
Objective of linear programming for an objective function is to
A
maximize or minimize.

B
subset or proper set modeling.

C
row or column modeling.

D
adjacent modeling.

Solution

In linear programming, the objective function is the linear equation which is representing some quantity (such as profit gained, cost, ...) which is to be maximized or minimized subject to the given constraints.
Question 2
1 / -0

If the feasible region for a solution of linear inequations is bounded, it is called as:

A
Concave Polygon

B
Finite Region

C
Convex Polygon

D
None of the above

Solution

A bounded feasible region will have both a maximum value and a minimum value for the objective function. It is bounded if it can be enclosed in any shape.
A convex polygon is a simple not self-intersecting closed shape in which no line segment between two points on the boundary ever goes outside the polygon.
Hence, the answer is convex polygon.
Question 3
1 / -0

If an iso-profit line yielding the optimal solution coincides with a constaint line, then

A
The solution is unbounded

B
The solution is infeasible

C
The constraint which coincides is redundant

D
None of the above

Solution

If an iso profit line which is yielding the optimal solution coincide with a constant line;then
$$\rightarrow$$ the solution will b bounded ,i.e there will be a definite bounded area where the solution would be optional.
$$\rightarrow$$ Since the area is bounded,the solution is feasible
$$\rightarrow $$And the constant which coincides is not a redundant
Hence None of above is the answer
Question 4
1 / -0

Graphical method can be used only when the decision variables is

A
more than 3.

B
more than 1.

C
Two

D
one

Solution

Graphical method can be used only when the decision variables is two.
Question 5
1 / -0

Objective of LPP is

A
A constraint

B
A function to be optimized

C
A relation between the variables

D
None of the above

Solution

The objective of Linear Programming Problems (LPP) is to minimize or maximize the function.
So, option B is correct.
Question 6
1 / -0

The shaded part of a given figure indicates the feasible region, then the constraints are

A
$$x,y\ge 0,x+y\ge 0,x\ge 5,y\le 3$$

B
$$x,y\ge 0,x-y\ge 0,x\le 5,y\le 3\quad $$

C
$$x,y\ge 0,x-y\ge 0,x\le 5,y\ge 3$$

D
$$x,y\ge 0,x-y\le 0,x\le 5,y\le 3$$

Solution

Now, as the graph is in first quadrant. So, $$x\ge 0,y\ge 0$$,
The region lies to the left of the line $$x=5$$, So $$ x\le 5$$
It lies below the line $$y=3$$, So $$y\le 3$$
Also, the region lies to the right of the line $$x=y$$. So, $$ x\ge y$$ or $$ x-y\ge 0$$
answer (b)
Question 7
1 / -0

The feasible solution of an LP problem, is ________

A
must satisfies all of the problem's constraints simultaneously

B
must be a corner point of the feasible region

C
need not satisfy all of the constraints, only some of them

D
must optimize the value of the objective function

Solution

the feasibe solution of a inear programming probem(LP) is a solution that must satisfy all of the problem's constraints simultaniously
Question 8
1 / -0

The corner points of the feasible region determined by the system of linear constraints are $$(0, 10),(5, 5), (25, 20)$$ and $$(0, 30)$$. Let $$Z = px + qy$$, where $$p, q > 0$$. Condition on $$p$$ and $$q$$ so that the maximum of $$Z$$ occurs at both the points $$(25, 20)$$ and $$(0, 30)$$ is _______.

A
$$5p = 2q$$

B
$$2p = 5q$$

C
$$p = 2q$$

D
$$q = 3p$$

Solution

Maximum of $$Z$$ occurs at $$(25,20)$$ and at $$(0,30)$$.
Hence, equating the vales of $$Z$$ at these points, we get
$$25p+20q=30q$$
$$\therefore 25p=10q$$
$$\therefore 5p=2q$$
This is the required relation.
Also as $$p,q>0$$, the value of $$Z$$ is always positive and hence, is greater at $$(25,20)$$ and at $$(0,30)$$ than at $$(0,10)$$ and $$(5,5)$$.
Question 9
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
What was the total number of black cars manufactured?

A
$$240$$

B
$$206$$

C
$$205$$

D
$$159$$

Solution

The number of Black cars manufactured

$$=$$ no. of black $$Vento$$ +no. of black $$Creta$$ +no. of black $$WagonR$$

$$=66+52+88 =206$$
Question 10
1 / -0

The taxi fare in a city is as follows: For the first kilometre, the fare is Rs. $$8$$ and the subsequent distance it is Rs. $$5$$ per km. Taking the distance covered as x km and fare as Rs y, write a linear equation.

A
$$y=4+6x$$

B
$$y=3+5x$$

C
$$y=4+5x$$

D
$$y=3+6x$$

Solution

for x km
$$ 1,km $$
fare
$$= 8$$
$$ (x-1)\,km $$
fare
$$ = (x - 1)5 $$
$$ y = 5(x - 1)+8 = 3 + 5x $$
B is correct

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

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

Linear Programming Test - 16

Result

Linear Programming Test - 16

Score

-

Rank

-

SHARING IS CARING

Question 1

maximize or minimize.

subset or proper set modeling.

row or column modeling.

adjacent modeling.

Solution

Question 2

Concave Polygon

Finite Region

Convex Polygon

None of the above

Solution

Question 3

The solution is unbounded

The solution is infeasible

The constraint which coincides is redundant

None of the above

Solution

Question 4

more than 3.

more than 1.

Two

one

Solution

Question 5

A constraint

A function to be optimized

A relation between the variables

None of the above

Solution

Question 6

$$x,y\ge 0,x+y\ge 0,x\ge 5,y\le 3$$

$$x,y\ge 0,x-y\ge 0,x\le 5,y\le 3\quad $$

$$x,y\ge 0,x-y\ge 0,x\le 5,y\ge 3$$

$$x,y\ge 0,x-y\le 0,x\le 5,y\le 3$$

Solution

Question 7

must satisfies all of the problem's constraints simultaneously

must be a corner point of the feasible region

need not satisfy all of the constraints, only some of them

must optimize the value of the objective function

Solution

Question 8

$$5p = 2q$$

$$2p = 5q$$

$$p = 2q$$

$$q = 3p$$

Solution

Question 9

$$240$$

$$206$$

$$205$$

$$159$$

Solution

Question 10

$$y=4+6x$$

$$y=3+5x$$

$$y=4+5x$$

$$y=3+6x$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.