Linear Programming Test

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Linear Programming Test - 21

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Question 1
1 / -0

To write the dual; it should be ensured that
I. All the primal variables are non-negative.
II. All the bi values are non-negative.
III. All the constraints are $$≤$$ type if it is maximization problem and $$≥$$ type if it is a minimization problem.

A
I and II

B
II and III

C
I and III

D
I, II and III

Solution

To write the dual, then all the primal variables must be non-negative.
All the constraints are $$\leq$$ type if it ia maximization problem and $$\geq$$ type if it is a minimization problem.
Question 2
1 / -0

Mark the wrong statement:

A
The primal and dual have equal number of variables.

B
The shadow price indicates the change in the value of the objective function, per unit increase in the value of the RHS.

C
The shadow price of a non-binding constraint is always equal to zero.

D
The information about shadow price of a constraint is important since it may be possible to purchase or, otherwise, acquire additional units of the concerned resource.

Solution

The number of variables in dual is equal to the number of constraints in the primal and the number of variables in primal is equal to the number of constraints in the dual.

Therefore, the primal and dual doesn't have equal number of variables.
Question 3
1 / -0

Which of the following statements about an LP problem and its dual is false?

A
If the primal and the dual both have optimal solutions, the objective function values for both problems are equal at the optimum

B
If one of the variables in the primal has unrestricted sign, the corresponding constraint in the dual is satisfied with equality

C
If the primal has an optimal solution, so has the dual

D
The dual problem might have an optimal solution, even though the primal has no (bounded) optimum

Solution

if one of the problems(primal, dual) is infeasible then the other problem is infeasible. Hence, the option D is the false statement.
Question 4
1 / -0

LP theory states that the optimal solution to any problem will lie at

A
the origin.

B
a corner point of the feasible region.

C
the highest point of the feasible region.

D
the lowest point in the feasible region.

E
none of the above

Solution

In linear programming, the optimal solution will occur at one or more corner points or on a line segment between two corner points. The corner points occurs only at the vertex of a feasible solution.
Question 5
1 / -0

Unboundedness is usually a sign that the LP problem.

A
has finite multiple solutions.

B
is degenerate.

C
contains too many redundant constraints.

D
has been formulated improperly.

E
none of the above.

Solution

A linear programming problem is said to have unbounded solution if it has infinite number of solutions. I.e., the problem has been formulated improperly
Question 6
1 / -0

An objective function in a linear program can be which of the following?

A
A maximization function

B
A nonlinear maximization function

C
A quadratic maximization function

D
An uncertain quantity

E
A divisible additive function

Solution

linear programming problem may be defined as the problem of maximizing or minimizing a linear function subject to linear constraints.
The objective function in a linear program is a maximization function.
Question 7
1 / -0

A point that satisfies all of a problem's constraints simultaneously is $$a(n)$$

A
maximum profit point.

B
corner point.

C
intersection of the profit line and a constraint.

D
intersection of two or more constraints.

E
None of the above

Solution

The set of all the points that satisfy all of the problem's constraints is called feasible region. The points which belong to this region are feasible points.

In the above figure, the shaded blue region is the feasible region. The points in this region are feasible points which satisfy all the constraints.
Question 8
1 / -0

Feasible region's optimal solution for a linear objective function always includes

A
downward point

B
upward point

C
corner point

D
front point

Solution

The vertex of the feasible solution is the corner point.
In the above figure, the blue shaded region is the feasible region and the points which highlighted in red color are the vertices of the feasible region which are called corner points.
Therefore, feasible region's optimal solution for linear objective function always includes corner point.
Question 9
1 / -0

While plotting constraints on a graph paper, terminal points on both the axes are connected by a straight line because:

A
the resources are limited in supply

B
the objective function as a linear function

C
the constraints are linear equations or inequalities

D
all of the above

Solution

The graph of the linear equation is a straight line.
If the terminal points are connected by a straight line then the given constraints are linear equations which may include inequalities.
Question 10
1 / -0

In linear programming context, sensitivity analysis is a technique to

A
Allocate resources optimally.

B
Minimize cost of operations.

C
Spell out relation between primal and dual.

D
Determine how optimal solution to LPP changes in response to problem inputs.

Solution

A sensitivity analysis is performed to determine the sensitivity of the solution to changes in parameters.
Option D is correct.

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Linear Programming Test - 21

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Linear Programming Test - 21

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Question 1

I and II

II and III

I and III

I, II and III

Solution

Question 2

The primal and dual have equal number of variables.

The shadow price indicates the change in the value of the objective function, per unit increase in the value of the RHS.

The shadow price of a non-binding constraint is always equal to zero.

The information about shadow price of a constraint is important since it may be possible to purchase or, otherwise, acquire additional units of the concerned resource.

Solution

Question 3

If the primal and the dual both have optimal solutions, the objective function values for both problems are equal at the optimum

If one of the variables in the primal has unrestricted sign, the corresponding constraint in the dual is satisfied with equality

If the primal has an optimal solution, so has the dual

The dual problem might have an optimal solution, even though the primal has no (bounded) optimum

Solution

Question 4

the origin.

a corner point of the feasible region.

the highest point of the feasible region.

the lowest point in the feasible region.

none of the above

Solution

Question 5

has finite multiple solutions.

is degenerate.

contains too many redundant constraints.

has been formulated improperly.

none of the above.

Solution

Question 6

A maximization function

A nonlinear maximization function

A quadratic maximization function

An uncertain quantity

A divisible additive function

Solution

Question 7

maximum profit point.

corner point.

intersection of the profit line and a constraint.

intersection of two or more constraints.

None of the above

Solution

Question 8

downward point

upward point

corner point

front point

Solution

Question 9

the resources are limited in supply

the objective function as a linear function

the constraints are linear equations or inequalities

all of the above

Solution

Question 10

Allocate resources optimally.

Minimize cost of operations.

Spell out relation between primal and dual.

Determine how optimal solution to LPP changes in response to problem inputs.

Solution

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