Question 1

A manager has only 200 tons of plastic for his company. This is an example of a(n)

Accepted Answer

The fact that the manager has only 200 tons of plastic is a constraint, as it limits the amount of plastic that can be used by the company.

Question 2

What most motivates a business to be concerned with efficient use of their resources?

Accepted Answer

Resources are limited and valuable. Efficient use of resources means that a business can maximize their output with the resources they have, without needing to increase their costs by acquiring more resources. This increases their profitability and competitiveness in the market.

Question 3

What is the goal in optimization?

Accepted Answer

In optimization, the ultimate goal is to find the decision variable values that result in the best possible objective function while satisfying all constraints. Option A is the only choice that correctly expresses this goal. Option B is incorrect because using all available resources may not always result in the best objective function. Option C is also incorrect because simply satisfying constraints may not necessarily yield the best outcome.

Question 4

A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is

Accepted Answer

An optimal solution is defined as a set of values for the decision variables that not only satisfy all the constraints but also yield the best (maximum or minimum) objective function value.

Question 5

The number of units to ship from Chicago to Memphis is an example of a(n)

Accepted Answer

The number of units to ship from one location to another is a decision that needs to be made in the context of logistics and supply chain management, making it an example of a decision.

Question 6

A production optimization problem has 4 decision variables and resource 1 limits how many of the 4 products can be produced. Which of the following constraints reflects this fact?

Accepted Answer

The constraint that reflects a limitation on production is typically an inequality showing that the production cannot exceed a certain limit, which is represented by $\le$.

Question 7

Which of the following is the general format of an objective function?

Accepted Answer

The general format of an objective function is to express it as a function of decision variables, often denoted as f(X₁, X₂, ..., Xₙ), without any inequality or equality constraints.

Question 8

A production optimization problem has 4 decision variables and a requirement that at least b₁ units of material 1 are consumed. Which of the following constraints reflects this fact?

Accepted Answer

This constraint states that the value of the objective function (F1F1F1S1) must be greater than or equal to the required minimum consumption of material 1 (b₁). This ensures that the optimization solution meets the minimum consumption requirement.

Question 9

Limited resources are modeled in optimization problems as

Accepted Answer

Limited resources are constraints in optimization problems. They limit the feasible region of the solution space and should be taken into account when finding optimal solutions.

Question 10

Which of the following fields of management science finds the optimal method of using resources to achieve the objectives of a business?

Accepted Answer

Mathematical programming is a field of management science that finds the optimal allocation of resources to achieve business objectives. It uses mathematical models to determine the best combination of inputs, such as labor and capital, to produce a desired output, such as profit or customer satisfaction. Simulation is used to model real-world situations and test different scenarios, regression is used to analyze relationships between variables, and discriminant analysis is used for classification purposes.

Question 11

A common objective when manufacturing printed circuit boards is

Accepted Answer

The objective is to minimize the total distance the drill bit must be moved to increase efficiency and reduce manufacturing time.

Question 12

A mathematical programming application employed by a shipping company is most likely

Accepted Answer

A shipping company would most likely use mathematical programming to solve routing and logistics problems, such as determining the most efficient routes for shipping goods or scheduling delivery times for multiple shipments. Product mix problems and manufacturing problems are more likely to be encountered by companies that produce goods rather than transport them, while financial planning problems are more commonly found in the finance industry.

Question 13

Most individuals manage their individual retirement accounts (IRAs) so they

Accepted Answer

Most individuals manage their IRAs to minimize the amount of taxes they must pay. This is because IRAs are tax-advantaged accounts, meaning contributions are made with pre-tax dollars and investments grow tax-free until withdrawal during retirement. Therefore, minimizing taxes is a key goal for many IRA account holders.

Question 14

Linear programming problems have

Accepted Answer

Linear programming problems have linear objective functions (i.e. the function to be maximized or minimized is a linear equation) and linear constraints (i.e. the constraints on the variables are all linear equations or inequalities). Therefore, the correct choice is D - linear objective functions, linear constraints.

Question 15

The desire to maximize profits is an example of a(n)

Accepted Answer

The desire to maximize profits is an objective, or a goal that a business aims to achieve, as opposed to a decision, constraint or parameter.

Question 16

Mathematical programming is referred to as

Accepted Answer

Mathematical programming involves optimizing a certain objective function subject to constraints, which makes it synonymous with optimization. Satisficing refers to choosing a satisfactory solution rather than an optimal one. Approximation involves finding an approximate solution to a problem. Simulation involves creating a model or scenario to observe outcomes or behavior in a controlled setting.

Question 17

What are the three common elements of an optimization problem?

Accepted Answer

The three common elements of an optimization problem are decisions, constraints, and an objective. These can be further explained as follows:
- Decisions refer to the choices or actions that need to be taken in order to achieve the desired outcome.
- Constraints are the limitations or restrictions that must be considered during the decision-making process.
- Objective is the goal or target that needs to be achieved, which is usually expressed in terms of maximizing or minimizing a certain quantity.

Question 18

A common objective in the product mix problem is

Accepted Answer

The common objective in the product mix problem is to maximize profit, as this will ultimately lead to the greatest financial success for the company. Maximizing cost or production volume may not necessarily lead to higher profits, while minimizing production time may not always be feasible or practical. Therefore, maximizing profit is the best choice for the objective in the product mix problem.

Question 19

Retail companies try to find

Accepted Answer

Retail companies often try to minimize their transportation costs, which involves finding the least costly method of transferring goods from warehouses to stores. By doing so, they can increase their profit margins and offer competitive pricing to consumers. Therefore, option A is the best choice.

Question 20

The symbols X₁, Z₁, Dog are all examples of

Accepted Answer

These symbols represent decision variables, which are the variables that decision-makers will choose values for in order to achieve the best outcome in a mathematical model or optimization problem. Constraints and objectives are parts of the model that describe the limitations and goals, respectively, while parameters are constants in the model.

Quiz 2: Introduction to Optimization and Linear Programming