Question 1

Large-scale optimization software can handle how many decision variables and constraints?
A)dozens
B)hundreds
C)thousands
D)millions
E)all of these answer choices are correct

Accepted Answer

Modern large-scale optimization software is designed to handle problems of varying sizes, from dozens to millions of decision variables and constraints, making all of these answer choices correct.

Question 2

If a firm is using a linear program to determine production amounts of its chairs and tables, which of the following constraints must be in the model?
A)non-negativity
B)labor hours
C)machine hours
D)profit maximization
E)wood availability

Accepted Answer

A

Question 3

What are the allowable constraint relationship types in optimization problems? A)<, >, = B)<, >, =, ≤, ≥ C)=, ≤, ≥ D)<, >, ≤, ≥ E)≠, =, ≤, ≥

Accepted Answer

C

Question 4

Which type of constraint does not allow the solution for a decision variable of an optimization problem to be less than zero?
A)negativity
B)positivity
C)anti-negativity
D)feasibility
E)non-negativity

Accepted Answer

Non-negativity constraint specifies that the decision variable of an optimization problem cannot be a negative value. It is expressed as x>=0. This constraint is useful in many real-life situations where negative values are not feasible or logical. Thus, the option E is the correct choice, and it is known as the non-negativity constraint.

Question 5

When formulating optimization problems, which of the following represent the typical sequence? 
A) (1)text-based formulation, (2)diagram, (3)algebraic formulation
B) (1)text-based formulation, (2)algebraic formulation, (3)diagram
C) (1)diagram, (2)algebraic formulation, (3)text-based formulation
D) (1)diagram, (2)text-based formulation, (3)algebraic formulation
E) (1)algebraic formulation, (2)diagram, (3)text-based formulation

Accepted Answer

The typical sequence for formulating optimization problems is to first create a diagram that illustrates the problem visually. Then, a text-based formulation can be developed to describe the problem in words. Finally, an algebraic formulation can be created to represent the problem mathematically. Therefore, the correct sequence is (1)diagram, (2)text-based formulation, (3)algebraic formulation, which is represented by choice D.

Question 6

Human intelligence is not needed in which of the following steps of solving optimization problems?
A)writing the problem formulation in words
B)writing the algebraic formulation of the problem
C)developing a spreadsheet model
D)solving the problem
E)interpreting the results

Accepted Answer

Human intelligence is not required for solving the problem once it has been properly formulated and set up, as this step can be performed by computers or algorithms designed for optimization.

Question 7

The algebraic formulation of an optimization problem must state what three things?
A)decision variables, random variables, and parameters
B)decision variables, random variables, and constraints
C)decision variables, random variables, and objective function
D)random variables, parameters, and objective function
E)decision variables, objective function, and constraints

Accepted Answer

The algebraic formulation of an optimization problem must state the decision variables, objective function, and constraints. Decision variables represent the unknown quantities that need to be determined. The objective function represents the goal of the optimization problem, which is either to maximize or minimize a specific quantity. Constraints represent the limitations or restrictions on the decision variables. Random variables and parameters may be used in certain types of optimization problems, but they are not essential components of the algebraic formulation.

Question 8

A ____________________ contains explicit definitions of the decision variables, an algebraic expression of the objective function, and algebraic statements of the constraints.
A)composition
B)derivation
C)manipulation
D)formulation
E)regurgitation

Accepted Answer

The definition matches the concept of mathematical formulation, which includes defining decision variables, the objective function, and the constraints in algebraic terms.

Question 9

A mathematical model in which one is trying to maximize or minimize some quantity while satisfying a set of constraints is a(n):
A)objective model
B)constrained model
C)constrained optimization problem
D)decision model
E)excel model

Accepted Answer

A mathematical model which involves optimizing a certain quantity while adhering to a set of restrictions or constraints is known as a constrained optimization problem. Option A is incorrect because "objective model" is a contradistinction to "subjective model" and isn't suitable in this case. Option B is incorrect because, while these types of models may include constraints or limitations, they do not always have an optimization component. Option D is incorrect because "decision model" is a general concept which could refer to any mathematical model that is used to aid decision-making. Option E is incorrect because "excel model" relates only to a specific software tool rather than to the broader category of mathematical modeling.

Question 10

Consider the following three functions: f(x)= 6x² G(x, y)=4x - 3y + 19 H(x, y)= 3xy Which of the following is true regarding the linearity of the functions? A)none of the functions is linear B)all three functions are linear C)g(x, y)is linear, but f(x)and h(x, y)are not linear D)g(x, y)and h(x, y)are linear, but f(x)is not linear E)h(x, y)is linear, but f(x)and g(x, y)are not linear

Accepted Answer

G(x, y) is linear because it is a first-degree polynomial in x and y. f(x) is not linear because it is a second-degree polynomial in x. H(x, y) is not linear because it involves the product of x and y.

Question 11

Once you've written the algebraic formulation of the problem, the next setup involved in Solving Optimization Problems is:
A)develop test cases
B)examine the results and make corrections
C)analyze and interpret the results
D)set up the Solver settings
E)write the problem formulation

Accepted Answer

Once the algebraic formulation of the problem has been written, the next step is to set up the Solver settings to solve the optimization problem. This involves selecting the appropriate Solver tool, setting the constraints and variables, and defining the objective function. Once the Solver settings have been established, the problem can be solved and the results can be analyzed and interpreted. Developing test cases and examining results and making corrections typically come later in the optimization process.

Question 12

The text-based formulation of an optimization problem should state what three things?
A)decision variables, random variables, and parameters
B)decision variables, objective function, and constraints
C)decision variables, random variables, and constraints
D)decision variables, random variables, and objective function
E)random variables, parameters, and objective function

Accepted Answer

The text-based formulation of an optimization problem should state the decision variables, objective function, and constraints. The decision variables are the variables that we can manipulate in the problem, the objective function is to be optimized, and the constraints restrict the values of the decision variables.

Question 13

In Linear Programming models, over what quantities do you have control?
A)decision variables
B)parameters
C)constraints
D)objective variables
E)coefficients

Accepted Answer

The decision variables are the quantities that the decision-maker has control over and can adjust to optimize the objective function. The parameters, constraints, objective variables, and coefficients are either constants or predetermined values that are known to the decision-maker and cannot be controlled or adjusted.

Question 14

What does LP stand for?
A)Linear Partition
B)Linear Program
C)Large-Scale Program
D)Linear Parameter
E)Linear Parallelism

Accepted Answer

LP commonly stands for Linear Program in the context of optimization and mathematics.

Question 15

Suppose that a firm makes gears (G)and axles (A). Each gear requires 15 minutes of labor and each axle requires 30 minutes of labor. One thousand hours of labor are available. How should the labor constraint(s)be written?
A)G + A ≤ 1000
B).25G + .5A ≤ 1000
C)G ≤ 15 and A ≤ 30
D).25G + .5A ≥ 1000
E)15G + 30A ≤ 1000

Accepted Answer

The labor constraint can be written as:

15G + 30A ≤ 1000 (total labor available is 1000 hours)

By dividing both sides by 60 to convert to hours, we can simplify the constraint to:

0.25G + 0.5A ≤ 16.67

Therefore, the correct choice is B: .25G + .5A ≤ 1000.

Question 16

A diagram of the situation can help _______ the problem as well as be a(n)______ _______ tool.
A)structure, valuable communication
B)define, algebraic development
C)bound, formulation development
D)unbound, formulation development
E)structure, unbounded formulation

Accepted Answer

A diagram can help structure the problem by visually organizing information and relationships. It can also be a valuable communication tool to convey ideas and concepts to others. None of the other options accurately describe the benefits of a diagram in problem-solving.

Question 17

If C represents the number of chairs produced, which of the following is a proper non-negativity constraint?
A)C ≠ 0
B)C > 0
C)C ≥ 0
D)C < 0
E)C ≤ 0

Accepted Answer

Non-negativity constraints in optimization problems allow variables to be zero or positive, making C ≥ 0 the correct choice.

Question 18

In Linear Programming models, what do you want to do with the objective?
A)upsize or downsize
B)rightsize or wrongsize
C)maximize or minimize
D)memorize
E)popularize

Accepted Answer

In Linear Programming models, we want to maximize or minimize the objective function, which represents the quantity that we want to optimize (e.g., profit, cost, production volume). Maximization is preferred when the objective represents a benefit (e.g., profit, revenue), while minimization is preferred when the objective represents a cost (e.g., production cost, transportation cost). Therefore, C is the best choice as it accurately describes what we want to do with the objective in Linear Programming models.

Question 19

Testing of the LP model should include __________ and _____________.
A)extreme case, base case
B)extreme case, test values
C)base case, minimum value
D)base case, test values
E)test value, maximum value

Accepted Answer

Testing of the LP model should include a base case, which is a scenario where all parameters are set at their expected values, and test values, which are scenarios where parameters are varied to ensure the model's robustness. Extreme cases may be useful in identifying the model's limitations or constraints, but they are not necessary for comprehensive testing. Additionally, including minimum or maximum values may not always be relevant depending on the specific problem being modeled.

Question 20

How can the following Linear Program be characterized?
 Min X + Y
Subject to
X ? 20
Y ? 5
X + Y ? 40
X, Y ? 0
A)bounded and feasible
B)unbounded and feasible
C)bounded and infeasible
D)unbounded and infeasible
E)this is not a Linear Program

Accepted Answer

The feasible region for this problem is the area bounded by X = 20, Y = 5, and the line X + Y = 40. This region is a triangular shape with vertices at (0, 5), (20, 0), and (20, 20). Since the objective function is to minimize X + Y, the optimal solution will occur at one of the vertices of this region. However, none of the vertices satisfy all the constraints, so the problem is infeasible.

Quiz 17: Spreadsheet Modeling: an Introduction

Large-scale optimization software can handle how many decision variables and constraints?

If a firm is using a linear program to determine production amounts of its chairs and tables, which of the following constraints must be in the model?

What are the allowable constraint relationship types in optimization problems?

Which type of constraint does not allow the solution for a decision variable of an optimization problem to be less than zero?

When formulating optimization problems, which of the following represent the typical sequence?

Human intelligence is not needed in which of the following steps of solving optimization problems?

The algebraic formulation of an optimization problem must state what three things?

A ____________________ contains explicit definitions of the decision variables, an algebraic expression of the objective function, and algebraic statements of the constraints.

A mathematical model in which one is trying to maximize or minimize some quantity while satisfying a set of constraints is a(n) :

Consider the following three functions: f(x) = 6x² G(x, y) =4x - 3y + 19 H(x, y) = 3xy Which of the following is true regarding the linearity of the functions?

Once you've written the algebraic formulation of the problem, the next setup involved in Solving Optimization Problems is:

The text-based formulation of an optimization problem should state what three things?

In Linear Programming models, over what quantities do you have control?

What does LP stand for?

Suppose that a firm makes gears (G) and axles (A) . Each gear requires 15 minutes of labor and each axle requires 30 minutes of labor. One thousand hours of labor are available. How should the labor constraint(s) be written?

A diagram of the situation can help _ the problem as well as be a(n) ___ tool.

If C represents the number of chairs produced, which of the following is a proper non-negativity constraint?

In Linear Programming models, what do you want to do with the objective?

Testing of the LP model should include and ___.

How can the following Linear Program be characterized? Min X + Y Subject to X ? 20 Y ? 5 X + Y ? 40 X, Y ? 0