Linear Programming Test

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Linear Programming Test - 4

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Question 1
1 / -0

In Corner point method for solving a linear programming problem the second step after finding the feasible region of the linear programming problem and determining its corner points is

A
Evaluate the objective function Z = ax + by at the center point

B
Evaluate the objective function Z = ax + by at each corner point.

C
Evaluate the objective function Z = ax + by at the mid points

D
None of these

Solution

In Corner point method for solving a linear programming problem the second step after finding the feasible region of the linear programming problem and determining its corner points is : To evaluate the objective function Z = ax + by at each corner point.
Question 2
1 / -0

In Corner point method for solving a linear programming problem one finds the feasible region of the linear programming problem ,determines its corner points and evaluates the objective function Z = ax + by at each corner point. If M and m respectively be the largest and smallest values at corner points then

A
If the feasible region is bounded, M and m respectively are the minimum and maximum values of the objective function

B
If the feasible region is unbounded, M and m respectively are the maximum and minimum values of the objective function

C
If the feasible region is bounded, M and m respectively are the maximum and minimum values of the objective function

D
None of these

Solution

In Corner point method for solving a linear programming problem one finds the feasible region of the linear programming problem ,determines its corner points and evaluates the objective function Z = ax + by at each corner point. If Mand m respectively be the largest and smallest values at corner points then If the feasible region is bounded, M and m respectively are the maximum and minimum values of the objective function .
Question 3
1 / -0

In Corner point method for solving a linear programming problem one finds the feasible region of the linear programming problem ,determines its corner points and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case feasible region is unbounded, M is the maximum value of the objective function if

A
The open half plane determined by ax + by > M has points in common with the feasible region

B
The open half plane determined by ax + by < M has no point in common with the feasible region

C
The open half plane determined by ax + by > M has no point in common with the feasible region

D
None of these

Solution

In Corner point method for solving a linear programming problem one finds the feasible region of the linear programming problem ,determines its corner points and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case feasible region is unbounded, M is the maximum value of the objective function if the open half plane determined by ax + by > M has no point in common with the feasible region . Otherwise, Z has no maximum value.
Question 4
1 / -0

In Corner point method for solving a linear programming problem one finds the feasible region of the linear programming problem ,determines its corner points and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case feasible region is unbounded, m is the minimum value of the objective function

A
if the open half plane determined by ax + by < m has points in common with the feasible region

B
if the open half plane determined by ax + by < m has no point in common with the feasible region

C
if the open half plane determined by ax + by > m has no point in common with the feasible region

D
None of these

Solution

In Corner point method for solving a linear programming problem one finds the feasible region of the linear programming problem ,determines its corner points and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case feasible region is unbounded, m is the minimum value of the objective function if the open half plane determined by ax + by < m has no point in common with the feasible region . Otherwise, Z has no minimum point.
Question 5
1 / -0

If two corner points of the feasible region are both optimal solutions of the same type, i.e., both produce the same maximum or minimum.

A
then any point on the line segment joining these two points is also an optimal solution of the opposite type

B
then any point on the line segment joining these two points is also an optimal solution of the same type

C
then no point on the line segment joining these two points is an optimal solution of the opposite type

D
then no point on the line segment joining these two points is an optimal solution of the same type

Solution

If two corner points of the feasible region are both optimal solutions of the same type, i.e., both produce the same maximum or minimum , then any point on the line segment joining these two points is also an optimal solution of the same type .
Question 6
1 / -0

In a LPP, the objective function is always

A
Cubic

B
Quadratic

C
Constant

D
Linear

Solution

In an LPP, the objective function is always linear. This is because these problems are always subjected to linear inequalities, where we maximise or minimise the linear functions.
Question 7
1 / -0

The optimal value of the objective function Z = ax + by may or may not exist, if the feasible region for a LPP is

A
A circle

B
Unbounded

C
A polygon

D
Bounded

Solution

The optimal value of the objective function Z = ax + by may or may not exist, if the feasible region for an LPP is unbounded. This is because the maximum or minimum value of the objective function may not exist. Even if it exists it must occur in a corner point of the feasible region.
Question 8
1 / -0

In an LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same

A
Minimum value

B
Mean value

C
Upper limit value

D
Maximum value

Solution

In an LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same maximum value . If the problem has multiple optimal solutions at the corner points, then both the points will have the same (maximum or minimum)value.
Question 9
1 / -0

In linear programming problems the function whose maxima or minima are to be found is called

A
Objective function

B
Selection function

C
Subjective function

D
Delta function

Solution

In linear programming problems the function whose maxima or minima are to be found is called Objective function . A linear function which has to be maximised or minimised is called as the linear objective function.
Question 10
1 / -0

In linear programming problems the optimum solution

A
satisfies a set of linear inequalities (called linear constraints)

B
satisfies a set of quadratic inequalities (called constraints)

C
satisfies a set of cubic inequalities (called constraints)

D
satisfies a set of piecewise – linear inequalities (called constraints)

Solution

In linear programming problems the optimum solution satisfies a set of linear inequalities (called linear constraints) .

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Linear Programming Test - 4

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Linear Programming Test - 4

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Question 1

Evaluate the objective function Z = ax + by at the center point

Evaluate the objective function Z = ax + by at each corner point.

Evaluate the objective function Z = ax + by at the mid points

None of these

Solution

Question 2

If the feasible region is bounded, M and m respectively are the minimum and maximum values of the objective function

If the feasible region is unbounded, M and m respectively are the maximum and minimum values of the objective function

If the feasible region is bounded, M and m respectively are the maximum and minimum values of the objective function

None of these

Solution

Question 3

The open half plane determined by ax + by > M has points in common with the feasible region

The open half plane determined by ax + by < M has no point in common with the feasible region

The open half plane determined by ax + by > M has no point in common with the feasible region

None of these

Solution

Question 4

if the open half plane determined by ax + by < m has points in common with the feasible region

if the open half plane determined by ax + by < m has no point in common with the feasible region

if the open half plane determined by ax + by > m has no point in common with the feasible region

None of these

Solution

Question 5

then any point on the line segment joining these two points is also an optimal solution of the opposite type

then any point on the line segment joining these two points is also an optimal solution of the same type

then no point on the line segment joining these two points is an optimal solution of the opposite type

then no point on the line segment joining these two points is an optimal solution of the same type

Solution

Question 6

Cubic

Quadratic

Constant

Linear

Solution

Question 7

A circle

Unbounded

A polygon

Bounded

Solution

Question 8

Minimum value

Mean value

Upper limit value

Maximum value

Solution

Question 9

Objective function

Selection function

Subjective function

Delta function

Solution

Question 10

satisfies a set of linear inequalities (called linear constraints)

satisfies a set of quadratic inequalities (called constraints)

satisfies a set of cubic inequalities (called constraints)

satisfies a set of piecewise – linear inequalities (called constraints)

Solution

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