Linear Programming Test

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Linear Programming Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

Minimise $$Z=\sum _{ j=1 }^{ n }{ \sum _{ i=1 }^{ m }{ { c }_{ ij }.{ x }_{ ij } } } $$
Subject to $$\sum _{ i=1 }^{ m }{ { x }_{ ij } } ={ b }_{ j },j=1,2,......n$$
$$\sum _{ j=1 }^{ n }{ { x }_{ ij } } ={ b }_{ j },j=1,2,......,m$$ is a LPP with number of constraints

A
$$m-n$$

B
$$mn$$

C
$$m+n$$

D
$$\cfrac { m }{ n } $$

Solution

Constraints will be
$${ x }_{ 11 }+{ x }_{ 21 }+.....+{ x }_{ m1 }={ b }_{ 1 }$$
$${ x }_{ 12 }+{ x }_{ 22 }+.....+{ x }_{ m2 }={ b }_{ 2 }$$
$${ x }_{ 1n }+{ x }_{ 2n }+.....+{ x }_{ mn }={ b }_{ n }$$
$${ x }_{ 11 }+{ x }_{ 12 }+.....+{ x }_{ 1n }={ b }_{ 1 }$$
$${ x }_{ 21 }+{ x }_{ 22 }+.....+{ x }_{ 2n }={ b }_{ 2 }\quad $$
$${ x }_{ m1 }+{ x }_{ m2 }+.....+{ x }_{ mn }={ b }_{ n }$$
So the total number of constraints $$=m+n$$
Question 2
1 / -0

The solution of the set of constraints of a linear programming problem is a convex (open or closed) is called ______ region.

A
feasible

B
active

C
linear

D
none of these
Question 3
1 / -0

Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that

A
The values of decision variables obtained by rounding off are always very close to the optimal values.

B
The value of the objective function for a maximization problem will likely be less than that for the simplex solution.

C
The value of the objective function for a minimization problem will likely be less than that for the simplex solution.

D
All constraints are satisfied exactly.

E
None of the above.

Solution

Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem, we find that the value of the objective function for a maximization problem will likely be less than that for the simplex solution.
Question 4
1 / -0

If a = b then ax = ...........

A
$$b + x$$

B
bx

C
b - x

D
$$b\, \div\, x$$

Solution

Given,
a = b
Multiplying both sides by x.
ax = bx
Question 5
1 / -0

The bar graph shows the grades obtained by a group of pupils in a test.
If grade C is the passing mark, how many pupils passed the test?

A
10

B
14

C
24

D
30

Solution

If grade $$C$$ is the paasing marks the, pupils from grade $$A$$ and grade $$B$$ has also passed the test.
$$\Rightarrow$$ Number of pupils obtained grade $$A$$ $$=6$$
$$\Rightarrow$$ Number of pupils obtained grade $$B$$ $$=10$$
$$\Rightarrow$$ Number of pupils obtained grade $$C$$ $$=14$$
$$\Rightarrow$$ Total number of pupils passed the test $$=6+10+14=30$$
Question 6
1 / -0

An iso-profit line represents

A
An infinite number of solutions all of which yield the same profit

B
An infinite number of solution all of which yield the same cost

C
An infinite number of optimal solutions

D
A boundary of the feasible region

Solution

The graph of the profit function is called an iso profit line. It is called this because iso means same or equal and the profit anywhere on the line is the same.
So, an iso-profit lines represents an infinite number of solutions all of which yield the same profit.
Question 7
1 / -0

In linear programming, lack of points for a solution set is said to

A
have no feasible solution

B
have a feasible solution

C
have single point method

D
have infinte point method

Solution

If there is no point in the feasible set, there is no feasible solution of the linear programming model.
In linear programming, lack of points for a solution set is said to have no feasible solution
Question 8
1 / -0

If x + y = 3 and xy = 2, then the value of $$\displaystyle x^{3}-y^{3}$$ is equal to

A
6

B
7

C
8

D
0

Solution

Formula used:
$$x^3-y^3=(x-y)(x^2+xy+y^2)$$
               $$=(\sqrt{(x+y)^2-4xy})[(x+y)^2-xy]$$
               $$=(\sqrt{(3)^2-4(2)})[(3)^2-2]$$
               $$=(\sqrt 1)(7)=7$$
Option B is correct.
Question 9
1 / -0

If the constraints in linear programming problem are changed

A
the problem is to be re-evaluated

B
solution is not defined

C
the objective function has to be modified

D
the change in constraints is ignored

Solution

The above question asks for the impact of change in constraints on the Linear programming problem. In this scenario, when there is a change in constraint, the solution will change definitely. Whether the solution exists or not, we can only find once the problem is re-evaluated.
In an LPP, the objective function is related to the main objective of any problem, either we have to maximize or minimize the function based on the situation whereas the constraints is related to physical restrictions in achieving the defined objective function. In real life problems, there might be situations when the constraints change, but objective function does not changes to accommodate the change in constraints.
Thus, if constraints in linear programming problem is changed, the problem has to be re-evaluated for the same objective function and after solving we can find whether the solution exists or not.
Question 10
1 / -0

The bar graph shows the number of cakes sold at a shop in four days.
What is the difference in number of cakes between the highest and the lowest daily sale?

A
20

B
35

C
30

D
40

Solution

We have to find the difference in number of cakes between the highest and the lowest daily sale.
The highest daily sale was on Sunday=45 cakes
The lowest daily sale was on Monday=25 cakes
Difference between highest and lowest daily sale Is 45-25=20 cakes.
So option A is the correct answer.

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Re-Attempt Weekly Quiz Competition

Linear Programming Test - 15

Result

Linear Programming Test - 15

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SHARING IS CARING

Question 1

$$m-n$$

$$mn$$

$$m+n$$

$$\cfrac { m }{ n } $$

Solution

Question 2

feasible

active

linear

none of these

Question 3

The values of decision variables obtained by rounding off are always very close to the optimal values.

The value of the objective function for a maximization problem will likely be less than that for the simplex solution.

The value of the objective function for a minimization problem will likely be less than that for the simplex solution.

All constraints are satisfied exactly.

None of the above.

Solution

Question 4

$$b + x$$

bx

b - x

$$b\, \div\, x$$

Solution

Question 5

10

14

24

30

Solution

Question 6

An infinite number of solutions all of which yield the same profit

An infinite number of solution all of which yield the same cost

An infinite number of optimal solutions

A boundary of the feasible region

Solution

Question 7

have no feasible solution

have a feasible solution

have single point method

have infinte point method

Solution

Question 8

6

7

8

0

Solution

Question 9

the problem is to be re-evaluated

solution is not defined

the objective function has to be modified

the change in constraints is ignored

Solution

Question 10

20

35

30

40

Solution

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