Linear Programming Test

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Linear Programming Test - 1

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Question 1
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A linear programming problem is one that is concerned with

A
finding the optimal value (maximum or minimum) of a linear function of several variables

B
finding the lower limit of a linear function of several variables

C
finding the limiting values of a linear function of several variables

D
finding the upper limits of a linear function of several variables

Solution

Explanation:

A linear programming problem is one that is concerned with finding the optimal value (maximum or minimum) of a linear function of several variables .
Question 2
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Which of the following types of problems cannot be solved by linear programming methods

A
Transportation problems

B
Traffic signal control

C
Manufacturing problems

D
Diet problems

Solution

Explanation:

Traffic signal control types of problems cannot be solved by linear programming methods, because there is no need for optimization in such problems.
Question 3
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In linear programming feasible region (or solution region) for the problem is

A
The common region determined by all the x ⩾ 0 and the objective function

B
The common region determined by all the objective functions including the non – negative constraints x ⩾ 0, y ⩾ 0

C
The common region determined by all the x ⩾ 0, y ⩾ 0 and the objective function

D
The common region determined by all the constraints including the non – negative constraints x ⩾ 0, y⩾ 0

Solution

Explanation:

In linear programming feasible region (or solution region) for the problem is given by the common region determined by all the constraints including the non – negative constraints x ⩾ 0, y ⩾ 0
Question 4
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In linear programming infeasible solutions

A
fall inside the a regular polygon

B
fall outside the feasible region

C
fall inside the feasible region

D
fall on the x = 0 plane

Solution

Explanation:

In linear programming infeasible solutions fall outside the feasible region . In other words, it the region other than the feasible region is called the infeasible region.
Question 5
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In linear programming, optimal solution

A
is not unique

B
satisfies all the constraints only

C
maximizes the objective function only

D
satisfies all the constraints as well as the objective function

Solution

Explanation:

In linear programming, any point in the feasible region which gives that gives the optimal value (maximum or minimum) of the objective function is called optimal solution. In other words, it satisfies all the constraints as well as the objective function .
Question 6
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Let R be the feasible region (convex polygon) for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), where the variables x and y are subject to constraints described by linear inequalities,

A
optimal value must occur at the centroid of the feasible region.

B
optimal value must occur at a corner point (vertex) of the feasible region.

C
None of these

D
optimal value must occur at the midpoints of the corner points (vertices) of the feasible region.

Solution

Explanation:

Let R be the feasible region (convex polygon) for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), where the variables x and y are subject to constraints described by linear inequalities then , optimal value must occur at a corner point (vertex) of the feasible region.
Question 7
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Let R be the feasible region for a linear programming problem, and let Z = ax + by be the objective function. If R is bounded, then

A
the objective function Z has only a minimum value on R

B
the objective function Z has both a maximum and a minimum value on R

C
the objective function Z has no minimum value on R

D
the objective function Z has only a maximum value on R

Solution

Explanation:

Let R be the feasible region for a linear programming problem, and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and each of these occur at the corner point (vertex) of R.
Question 8
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Let R be the feasible region for a linear programming problem,and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and

A
each of these occurs at the centre of R.

B
each of these occurs at some points except corner points of R.

C
each of these occurs at themidpoints of the edges of R

D
each of these occurs at a corner point (vertex) of R.

Solution

Explanation:

Let R be the feasible region for a linear programming problem,and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and each of these occurs at a corner point (vertex) of R.
Question 9
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A maximum or a minimum may not exist for a linear programming problem if

A
The feasible region is unbounded

B
if the constraints are non linear

C
if the objective function is continuous

D
The feasible region is bounded

Solution

Explanation:

A maximum or a minimum may not exist for a linear programming problem if The feasible region is unbounded .
Question 10
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In Corner point method for solving a linear programming problem the first step is to

A
Find the feasible region of the linear programming problem and determine its corner points (vertices).

B
Find the feasible region of the linear programming problem and determine its center points (vertices).

C
Find the infeasible regions of the linear programming problem and determine theunion of the infeasible regions

D
Find the infeasible region of the linear programming problem and determine its complement

Solution

Explanation:

In Corner point method for solving a linear programming problem the first step is : To find the feasible region of the linear programming problem and determine its corner points (vertices) either by inspection or by solving the two equations of the lines intersecting at that point.

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Linear Programming Test - 1

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Linear Programming Test - 1

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SHARING IS CARING

Question 1

finding the optimal value (maximum or minimum) of a linear function of several variables

finding the lower limit of a linear function of several variables

finding the limiting values of a linear function of several variables

finding the upper limits of a linear function of several variables

Solution

Question 2

Transportation problems

Traffic signal control

Manufacturing problems

Diet problems

Solution

Question 3

The common region determined by all the x ⩾ 0 and the objective function

The common region determined by all the objective functions including the non – negative constraints x ⩾ 0, y ⩾ 0

The common region determined by all the x ⩾ 0, y ⩾ 0 and the objective function

The common region determined by all the constraints including the non – negative constraints x ⩾ 0, y⩾ 0

Solution

Question 4

fall inside the a regular polygon

fall outside the feasible region

fall inside the feasible region

fall on the x = 0 plane

Solution

Question 5

is not unique

satisfies all the constraints only

maximizes the objective function only

satisfies all the constraints as well as the objective function

Solution

Question 6

optimal value must occur at the centroid of the feasible region.

optimal value must occur at a corner point (vertex) of the feasible region.

None of these

optimal value must occur at the midpoints of the corner points (vertices) of the feasible region.

Solution

Question 7

the objective function Z has only a minimum value on R

the objective function Z has both a maximum and a minimum value on R

the objective function Z has no minimum value on R

the objective function Z has only a maximum value on R

Solution

Question 8

each of these occurs at the centre of R.

each of these occurs at some points except corner points of R.

each of these occurs at themidpoints of the edges of R

each of these occurs at a corner point (vertex) of R.

Solution

Question 9

The feasible region is unbounded

if the constraints are non linear

if the objective function is continuous

The feasible region is bounded

Solution

Question 10

Find the feasible region of the linear programming problem and determine its corner points (vertices).

Find the feasible region of the linear programming problem and determine its center points (vertices).

Find the infeasible regions of the linear programming problem and determine theunion of the infeasible regions

Find the infeasible region of the linear programming problem and determine its complement

Solution

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