Question 1

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

Accepted Answer

C

Question 2

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

Formulation is the process of defining and analyzing a problem in order to create a mathematical model that represents the problem's key characteristics. This model is composed of decision variables, an objective function, and constraints. Therefore, the correct choice is D) formulation.

Question 3

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 restricts the decision variable to be zero or greater than zero. This is a common constraint in optimization problems as negative values for decision variables do not make physical sense in many cases.

Question 4

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 5

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 that involves optimizing an objective function while satisfying a set of constraints is known as a constrained optimization problem. Option A, objective model, is a vague term that may refer to any model with an objective function, regardless of constraints. Option B, constrained model, is also vague and does not convey the optimization aspect of the problem. Option D, decision model, is too broad and could refer to any model involving decision-making, which may not necessarily involve optimization. Option E, excel model, is a tool for constructing and manipulating mathematical models but does not describe the nature of the model itself.

Question 6

Sausage and Cheese Ltd.prepares three gift packages containing sausages and cheeses.The "Tasters," "Succulent," and "Gourmet" gift packages contain 3 sausages and 6 cheeses,5 sausages and 4 cheeses,and 6 sausages and 5 cheeses,respectively.There are 2500 sausages and 3000 cheeses available for packing,and demand is unlimited.Profits are $2.50,$3.50,and $4.00 for the "Tasters," "Succulent," and "Gourmet" gift packages,respectively.The goal is to maximize profits.Let T,S,and G represent the number of gift packages produced of type "Tasters," "Succulent," and "Gourmet," respectively.What is the objective function for this linear program?
A)Max T + S + G
B)Max 2.5T + 3.5S + 4G
C)Min T + S + G
D)Max 10(T + S + G)
E)Max 9T + 9S + 11G

Accepted Answer

The objective function represents the total profit, which is calculated by multiplying the number of gift packages of each type by their respective profits and adding them together. Therefore, the objective function is: Max 2.5T + 3.5S + 4G. Option A only considers the number of gift packages produced without considering profits. Options C and D are not appropriate as they are minimizing the number of gift packages or maximizing a value that does not correspond to profits. Option E uses incorrect profit values. Therefore, the best choice is B.

Question 7

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 three components of an optimization problem are decision variables, objective function, and constraints. Decision variables are the quantities that can be varied in the problem, objective function defines the quantity to be optimized, and constraints specify the limitations or restrictions of the problem. Random variables and parameters may also be present in the problem but they are not necessary components for every optimization problem.

Question 8

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

Accepted Answer

LP stands for Linear Programming, which is an optimization technique used in mathematics and computer science to find the best solution to a problem with linear constraints.

Question 9

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

Since each gear requires 15 minutes and each axle requires 30 minutes of labor, we can write the labor constraint as follows: 
0.25 hours (15 minutes) of labor is required for each gear, and 0.5 hours (30 minutes) of labor is required for each axle. Let G be the number of gears produced and A be the number of axles produced. Thus, the total amount of labor used is 0.25G + 0.5A. Since there are 1000 hours of labor available, the labor constraint can be written as:
0.25G + 0.5A ≤ 1000

Question 10

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

Decision variables are the quantities over which the decision-maker has control and are the inputs to the objective function. Parameters are fixed values, coefficients are the values that multiply the decision variables in the objective function and constraints, and objective variables are the output of the problem. Therefore, the decision-maker has control only over the decision variables.

Question 11

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 formulation of an optimization problem must include the decision variables (the variables we want to choose to optimize our objective), the objective function (the function we want to optimize, usually either maximize or minimize), and the constraints (the limitations we have that restrict the values of the decision variables). Random variables and parameters are not necessary components of the formulation, although they may appear in certain types of optimization problems.

Question 12

Sausage and Cheese Ltd.prepares three gift packages containing sausages and cheeses.The "Tasters," "Succulent," and "Gourmet" gift packages contain 3 sausages and 6 cheeses,5 sausages and 4 cheeses,and 6 sausages and 5 cheeses,respectively.There are 2500 sausages and 3000 cheeses available for packing,and demand is unlimited.Profits are $2.50,$3.50,and $4.00 for the "Tasters," "Succulent," and "Gourmet" gift packages,respectively.The goal is to maximize profits.Let T,S,and G represent the number of gift packages produced of type "Tasters," "Succulent," and "Gourmet," respectively.What is the constraint describing the sausage capacity?
A)2.5T + 3.5S + 4G ≤ 2500
B)3T + 5S + 6G ≥ 2500
C)9T + 9S + 11G ≤ 2500
D)0.8333T + 1.9444S + 2.1818G ≤ 2500
E)3T + 5S + 6G ≤ 2500

Accepted Answer

The constraint describing the sausage capacity is the sum of sausages used in each type of gift package must be less than or equal to the total number of sausages available: 
3T + 5S + 6G ≤ 2500. 
To maximize profits, we need to use as many resources as possible, so we want to use up all the sausages available without going over the limit. Choice (E) represents this constraint.

Question 13

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 is written, the next step is to set up the Solver settings. This involves specifying the variables, constraints, and the objective function in the Solver tool and selecting the appropriate Solver algorithm to find the optimal solution. The other options listed, such as developing test cases, analyzing and interpreting the results, and making corrections, are steps that would occur after the Solver has been run and a result has been obtained. Writing the problem formulation is also a step that would have already been completed at the beginning of the process.

Question 14

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, the objective is either to maximize profit, revenue, or some other measure of success or to minimize costs, time, or resources utilized. Therefore, the best choice is to maximize or minimize the objective function.

Question 15

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 answer of When formulating optimization problems,which of the following...

Question 16

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 covers the normal expected scenario, and test values, which cover a range of scenarios to ensure the model performs well under different conditions. Extreme cases, minimum or maximum values, are also useful to test the model's robustness and ability to handle outliers or unexpected inputs but are not necessary for all LP models.

Question 17

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 18

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

The answer of If a firm is using a linear...

Question 19

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

Large-scale optimization software is designed to handle problems with a high number of decision variables and constraints. Therefore, it can handle problems with dozens, hundreds, thousands, or even millions of decision variables and constraints.

Question 20

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 providing a visual representation of the situation, and it can also be a valuable communication tool for explaining the problem to others. Choices B, C, D, and E do not accurately describe how a diagram can help solve a problem.

Quiz 18: Introduction to Optimization

What are the allowable constraint relationship types in optimization problems?

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

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

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

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

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

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?

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

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

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

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

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

Testing of the LP model should include and ___.

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

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?

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

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