Question 1

Coordinates of all corner points are substituted into the objective function when we use the approach called
A)least squares.
B)regression.
C)enumeration.
D)graphical linear programming.
E)constraint assignment.

Accepted Answer

Enumeration is a method for solving optimization problems by systematically evaluating all possible solutions and selecting the one with the best objective function value.

Question 2

In the range of feasibility, the value of the shadow price remains constant.

Accepted Answer

The shadow price, or dual value, of a constraint in linear programming represents the rate of change in the objective function per unit increase in the right-hand side of the constraint, and it remains constant as long as the basis of the optimal solution does not change, which happens within the range of feasibility for that constraint.

Question 3

When a change in the value of an objective function coefficient remains within the range of optimality, the optimal solution also remains the same.

Accepted Answer

When a change in the value of an objective function coefficient remains within the range of optimality, the optimal solution (in terms of the values of the decision variables that optimize the objective function) does not change, because the solution remains feasible and optimal within this range.

Question 4

Which of the following choices constitutes a simultaneous solution to these equations?

A)x = 1, y = 1.5
B)x = .5, y = 2
C)x = 0, y = 3
D)x = 2, y = 0
E)x = 0, y = 0

Accepted Answer

The answer of Which of the following choices constitutes a...

Question 5

Which of the following is not a component of the structure of a linear programming model?
A)constraints
B)decision variables
C)parameters
D)a goal or objective
E)environmental uncertainty

Accepted Answer

Environmental uncertainty is not a component of the structure of a linear programming model. Linear programming models consist of an objective function, decision variables, constraints, and parameters, all of which are assumed to be known with certainty.

Question 6

Using the enumeration approach, optimality is obtained by evaluating every coordinate.

Accepted Answer

The enumeration approach involves evaluating every possible solution to find the optimal one, not just every coordinate.

Question 7

Which objective function has the same slope as this one: $4 x + $2 y = $20?
A)$4 x + $2 y = $10
B)$2 x + $4 y = $20
C)$2 x − $4 y = $20
D)$4 x − $2 y = $20
E)$8 x + $8 y = $20

Accepted Answer

The slope of a line in a two-dimensional plane is determined by the coefficients of x and y when the equation is in the form of y = mx + b. The given equation and choice A have the same coefficients for x and y, meaning they have the same slope. Changing the constant on the right side of the equation does not affect the slope.

Question 8

Every change in the value of an objective function coefficient will lead to changes in the optimal solution.

Accepted Answer

The optimal solution may remain unchanged for certain ranges of changes in the objective function coefficients, a concept known as the range of optimality in sensitivity analysis.

Question 9

For the constraints given below, which point is in the feasible solution space of this minimization problem?

A)x = .5, y = 5
B)x = 0, y = 4
C)x = 2, y = 5
D)x = 1, y = 2
E)x = 2, y = 1

Accepted Answer

The answer of For the constraints given below, which point...

Question 10

The region which satisfies all of the constraints in graphical linear programming is called the
A)optimum solution space.
B)region of optimality.
C)lower left hand quadrant.
D)region of non-negativity.
E)feasible solution space.

Accepted Answer

The feasible solution space in graphical linear programming refers to the area or region on the graph that satisfies all of the constraints of the problem. This is where all possible solutions that meet the given conditions are found, but it does not necessarily indicate the optimal solution.

Question 11

The logical approach, from beginning to end, for assembling a linear programming model begins with
A)identifying the decision variables.
B)identifying the objective function.
C)specifying the objective function parameters.
D)identifying the constraints.
E)specifying the constraint parameters.

Accepted Answer

The logical approach to assembling a linear programming model starts with identifying the decision variables, as they are the foundation upon which the objective function and constraints are built.

Question 12

In graphical linear programming, when the objective function is parallel to one of the binding constraints, then
A)the solution is suboptimal.
B)multiple optimal solutions exist.
C)a single corner point solution exists.
D)no feasible solution exists.
E)the constraint must be changed or eliminated.

Accepted Answer

When the objective function is parallel to one of the binding constraints in graphical linear programming, it indicates that there are multiple points along that constraint line that will give the same optimal value for the objective function, hence multiple optimal solutions exist.

Question 13

Nonbinding constraints are not associated with the feasible solution space; i.e., they are redundant and can be eliminated from the matrix.

Accepted Answer

Nonbinding constraints are part of the feasible solution space but do not affect the optimal solution. They are not redundant and cannot always be eliminated without potentially altering the feasible region.

Question 14

Which of the following choices constitutes a simultaneous solution to these equations?

A)x = 2, y = .5
B)x = 4, y = −.5
C)x = 2, y = 1
D)x = y
E)y = 2 x

Accepted Answer

The answer of Which of the following choices constitutes a...

Question 15

Which of the following could not be a linear programming problem constraint?
A)1 A + 2 B ≤ 3
B)1 A + 2 B ≥ 3
C)1 A + 2 B = 3
D)1 A + 2 B + 3 C + 4 D ≤ 5
E)1 A + 2 B

Accepted Answer

Linear programming problem constraints must involve inequality or equality relations between linear expressions. Option E, "1 A + 2 B," lacks such a relation, making it not a valid constraint.

Question 16

Nonzero slack or surplus is associated with a binding constraint.

Accepted Answer

Nonzero slack or surplus is associated with a non-binding constraint, as it indicates that the constraint is not exactly met but has some leeway.

Question 17

What combination of x and y will yield the optimum for this problem?

A)x = 2, y = 0
B)x = 0, y = 0
C)x = 0, y = 3
D)x = 1, y = 2.5
E)x = 0, y = 4

Accepted Answer

The answer of What combination of x and y will...

Question 18

In graphical linear programming to maximize profit, the objective function is:
(I)a family of parallel lines.(II)a family of isoprofit lines.(III)interpolated.(IV)linear.
A)I only
B)II only
C)III and IV only
D)I, II, and IV only
E)I, II, III, and IV

Accepted Answer

The objective function in graphical linear programming to maximize profit is represented by a family of parallel lines (I), which are also known as isoprofit lines (II), and these lines are linear (IV). Interpolation (III) is not a characteristic of the objective function itself but a method that might be used in solving linear programming problems.

Question 19

For the products A, B, C, and D, which of the following could be a linear programming objective function?
A)Z = 1 A + 2 B + 3 C + 4 D
B)Z = 1 A + 2 BC + 3 D
C)Z = 1 A + 2 AB + 3 ABC + 4 ABCD
D)Z = 1 A + 2 B ÷ C + 3 D
E)Z = 1 A + 2 B − 1 CD

Accepted Answer

Linear programming objective functions are linear, meaning they consist of variables that are either added or subtracted, each multiplied by a constant. Option A is the only choice that fits this description, as it involves a simple linear combination of the variables A, B, C, and D.

Question 20

For a linear programming problem with the following constraints, which point is in the feasible solution space assuming this is a maximization problem?

A)x = 1, y = 5
B)x = −1, y = 1
C)x = 4, y = 4
D)x = 2, y = 1
E)x = 2, y = 8

Accepted Answer

The answer of For a linear programming problem with the...

Quiz 19: Linear Programming

Coordinates of all corner points are substituted into the objective function when we use the approach called

In the range of feasibility, the value of the shadow price remains constant.

When a change in the value of an objective function coefficient remains within the range of optimality, the optimal solution also remains the same.

Which of the following choices constitutes a simultaneous solution to these equations?

Which of the following is not a component of the structure of a linear programming model?

Using the enumeration approach, optimality is obtained by evaluating every coordinate.

Which objective function has the same slope as this one: $4 x + $2 y = $20?

Every change in the value of an objective function coefficient will lead to changes in the optimal solution.

For the constraints given below, which point is in the feasible solution space of this minimization problem?

The region which satisfies all of the constraints in graphical linear programming is called the

The logical approach, from beginning to end, for assembling a linear programming model begins with

In graphical linear programming, when the objective function is parallel to one of the binding constraints, then

Nonbinding constraints are not associated with the feasible solution space; i.e., they are redundant and can be eliminated from the matrix.

Which of the following choices constitutes a simultaneous solution to these equations?

Which of the following could not be a linear programming problem constraint?

Nonzero slack or surplus is associated with a binding constraint.

What combination of x and y will yield the optimum for this problem?

In graphical linear programming to maximize profit, the objective function is: (I) a family of parallel lines.(II) a family of isoprofit lines.(III) interpolated.(IV) linear.

For the products A, B, C, and D, which of the following could be a linear programming objective function?

For a linear programming problem with the following constraints, which point is in the feasible solution space assuming this is a maximization problem?