Decision Mathematics 1 Quizzes: Master Decision-Making Skills

Question 1

Which ethical concern arises from using mathematical models in decision-making?

Accepted Answer

Models may introduce or reinforce biases, leading to unfair or discriminatory outcomes.

Answer

Models always provide accurate and unbiased predictions.

Answer

Models are only useful in highly technical fields.

Answer

Ethical considerations are not relevant when using mathematical models.

Question 2

In Markov chains, a defining characteristic is that:

Accepted Answer

The next state depends only on the current state, not on past states.

Answer

The system always reaches a stable state.

Answer

Transition probabilities change over time.

Answer

Markov chains can only be used for systems that change continuously.

Question 3

Which of the following is NOT an assumption of linear programming?

Accepted Answer

Certainty

Answer

Proportionality

Answer

Non-negativity

Answer

Additivity

Question 4

In a zero-sum game, the total payoff to all players is always:

Accepted Answer

Zero

Answer

Positive

Answer

Negative

Answer

Uncertain

Question 5

Which of the following is a method for solving a two-player, zero-sum game?

Accepted Answer

Dominance

Answer

Linear programming

Answer

Network analysis

Answer

Monte Carlo simulation

Question 6

The critical path of a project network is the:

Accepted Answer

Longest path from the start node to the end node.

Answer

Shortest path from the start node to the end node.

Answer

Path with the most activities.

Answer

Path with the least amount of slack.

Question 7

In a transportation network, the objective function typically minimizes:

Accepted Answer

Total cost of transportation

Answer

Total distance traveled

Answer

Total time of transportation

Answer

Number of vehicles required

Question 8

What is the difference between a deterministic model and a stochastic model in decision mathematics?

Accepted Answer

Deterministic models use fixed data, while stochastic models use random data.

Answer

Deterministic models are more accurate than stochastic models.

Answer

Stochastic models are more complex than deterministic models.

Answer

There is no difference between deterministic and stochastic models.

Question 9

What is the main purpose of decision mathematics?

Accepted Answer

To aid in making optimal decisions under various conditions.

Answer

To predict the future with certainty.

Answer

To eliminate uncertainty completely.

Answer

To maximize profits in all scenarios.

Question 10

Which of the following is not a fundamental concept of decision mathematics, the study of mathematical models for decision-making?

Accepted Answer

Calculus

Answer

Linear programming

Answer

Game theory

Answer

Network analysis

Question 11

Which of the following is a primary benefit of studying decision mathematics?

Accepted Answer

Developing critical thinking and problem-solving skills

Answer

Memorizing mathematical formulas

Answer

Solving abstract equations

Answer

Understanding historical mathematics

Question 12

What is the primary goal of linear programming, a technique used to optimize decisions?

Accepted Answer

To find the optimal solution to a linear function

Answer

To solve systems of equations

Answer

To determine the area of a triangle

Answer

To calculate the volume of a sphere

Question 13

In a zero-sum game, where the gains of one player are balanced by the losses of the others, what is the sum of the payoffs to all players?

Accepted Answer

Zero

Answer

Always positive

Answer

Always negative

Answer

Unknown

Question 14

What is the key distinction between decision mathematics and traditional mathematics?

Accepted Answer

Decision mathematics focuses on solving real-world problems, while traditional mathematics is more abstract.

Answer

Traditional mathematics is only applicable to economics.

Answer

There is no difference between the two.

Answer

Decision mathematics requires extensive computational power.

Question 15

Which of the following is a key skill developed through the study of decision mathematics?

Accepted Answer

Problem-solving

Answer

Memorization

Answer

Algebraic manipulation

Answer

Calculus

Question 16

How can decision mathematics be used to improve decision-making?

Accepted Answer

By providing quantitative analysis of options

Answer

By eliminating uncertainty

Answer

By guaranteeing the best possible outcome

Answer

By making decisions for individuals

Question 17

A network has the following adjacency matrix:
	A	B	C
	A	0	1	0
	B	1	0	1
	C	0	1	0
Determine if the network is connected.

Accepted Answer

Yes, the network is connected.

Answer

No, the network is not connected.

Answer

Cannot be determined from the given information.

Question 18

One of the criticisms of the internal rate of return (IRR) method is:

Accepted Answer

Potential for multiple IRRs

Answer

Difficulty in calculation

Answer

Omission of time value of money

Answer

Applicability only to short-term projects

Question 19

A spanning tree is a subgraph of a connected graph that:

Accepted Answer

Contains all the vertices but not all the edges of the original graph

Answer

Contains all the vertices and edges of the original graph

Answer

Contains all the edges but not all the vertices of the original graph

Answer

Is a cycle

Question 20

Which fundamental concept of decision mathematics involves optimizing resource allocation and decision-making?

Accepted Answer

Linear programming

Answer

Calculus

Answer

Algebra

Answer

Statistics

Question 21

In game theory, a scenario where each player's best course of action relies on the actions of other players is called:

Accepted Answer

Nash equilibrium

Answer

Maximin strategy

Answer

Minimax strategy

Answer

Dominant strategy

Question 22

In a linear programming problem, what is the primary purpose of the objective function?

Accepted Answer

To express the quantity that is being optimized (either maximized or minimized).

Answer

To represent the constraints that limit the possible solutions.

Answer

To provide a method for solving the linear programming problem.

Answer

To describe the set of all feasible solutions to the problem.

Question 23

In a linear programming problem, which of the following is the correct form of the objective function?

Accepted Answer

Maximizing a linear combination of variables

Answer

Maximizing the difference between two variables

Answer

Minimizing the absolute value of a variable

Question 24

In a non-zero-sum game, how do the gains and losses of the players relate?

Accepted Answer

They are not necessarily equal.

Answer

They are always equal.

Answer

The gains of one player equal the losses of the other.

Answer

The losses of one player are always greater than the gains of the other.

Question 25

In game theory, a game where each player's strategy depends on the strategies of the other players is known as a:

Accepted Answer

Non-cooperative game

Answer

Zero-sum game

Answer

Cooperative game

Answer

Sequential game

Question 26

In a network analysis problem, the number of edges that connect a vertex to the rest of the network is referred to as its:

Accepted Answer

Degree

Answer

Eccentricity

Answer

Closeness

Answer

Betweenness

Question 27

In a zero-sum game, the total gains of all players:

Accepted Answer

Must sum to zero

Answer

Are always positive

Answer

Are always negative

Answer

Cannot be determined

Question 28

Which of the following algorithms is used to solve transportation problems?

Accepted Answer

Hungarian method

Answer

Simplex method

Answer

Dijkstra's algorithm

Answer

Floyd-Warshall algorithm

Question 29

Which of the following measures the average distance of a vertex from all other vertices in a network?

Accepted Answer

Closeness

Answer

Degree

Answer

Eccentricity

Answer

Betweenness

Question 30

Decision mathematics is useful for:

Accepted Answer

Making informed decisions in various fields

Answer

Predicting future outcomes with certainty

Answer

Eliminating all risk from decision-making

Answer

Solving all problems instantly

Question 31

Which of the following key concepts is NOT included in Decision Mathematics 1?

Accepted Answer

Calculus

Answer

Linear programming

Answer

Game theory

Answer

Network analysis

Question 32

In a two-person zero-sum game, if the payoff of one player increases, the payoff of the other player:

Accepted Answer

Decreases

Answer

Increases

Answer

Remains the same

Answer

Cannot be determined

Question 33

A connected network consists of six nodes and seven edges. What is the minimum spanning tree of the network?

Accepted Answer

A tree with six edges

Answer

A tree with seven edges

Answer

A tree with five edges

Answer

A tree with four edges

Question 34

In the business world, what is a practical application of linear programming?

Accepted Answer

Optimizing resource allocation to maximize production

Answer

Predicting future customer demand

Answer

Evaluating the effectiveness of marketing campaigns

Question 35

In a transportation problem with multiple origins and destinations, what is the primary objective?

Accepted Answer

Minimize the total transportation cost while meeting supply and demand constraints.

Answer

Maximize the total supply of the commodity.

Answer

Ensure that all origins supply an equal amount of the commodity.

Question 36

Which of the following is not a concept covered in Decision Mathematics 1?

Accepted Answer

Calculus

Answer

Linear programming

Answer

Game theory

Answer

Network analysis

Question 37

In a linear programming problem, what does the objective function represent?

Accepted Answer

The goal to be achieved (maximized or minimized)

Answer

The constraints that the variables must meet

Answer

The decision variables

Answer

The relationships between decision variables

Question 38

Which characteristic applies to non-zero-sum games?

Accepted Answer

The total gains of all players can be negative

Answer

The gains of one player are balanced by the losses of others

Answer

The players' strategies are independent

Answer

The number of players is always odd

Question 39

In network analysis, the critical path refers to:

Accepted Answer

The path with the least amount of slack (float)

Answer

The longest path from the start to the end node

Answer

The shortest path from the start to the end node

Answer

The path with the most resources allocated

Question 40

Which technique is commonly used to solve linear programming problems?

Accepted Answer

Simplex method

Answer

Graphical method

Answer

Numerical integration

Answer

Regression analysis

Question 41

The Nash equilibrium in a game means that:

Accepted Answer

No player can improve their outcome by unilaterally changing their strategy

Answer

All players have the same payoff

Answer

The total payoff to all players is maximized

Answer

The game is zero-sum

Question 42

In network analysis, what does a node represent?

Accepted Answer

An event or activity

Answer

A resource or constraint

Answer

A decision point

Answer

A path between two nodes

Question 43

How is the expected value of a decision calculated?

Accepted Answer

Sum of the products of each outcome and its probability

Answer

Average of all possible outcomes

Answer

Most likely outcome

Answer

Outcome with the highest payoff

Question 44

Which of the following is an advantage of using decision mathematics?

Accepted Answer

Improves decision-making

Answer

Increases memorization

Answer

Reduces creativity

Answer

Wastes time

Question 45

Which of the following is a limitation of decision mathematics?

Accepted Answer

Cannot handle all types of problems

Answer

Provides optimal solutions

Answer

Always accurate

Answer

Easy to use

Question 46

In a zero-sum game, the algebraic sum of the players' payoffs is always:

Accepted Answer

Zero

Answer

Negative

Answer

Positive

Answer

Indeterminate

Question 47

Which of the following best exemplifies a network problem?

Accepted Answer

Determining the shortest path between two locations on a map.

Answer

Selecting the most profitable investment portfolio.

Answer

Maximizing the production output of a factory.

Answer

Solving a system of linear equations.

Question 48

What is an advantage of incorporating decision trees in decision-making?

Accepted Answer

They provide a visual representation and simplify the decision-making process.

Answer

They can only be used to address simple and straightforward decisions.

Answer

They consistently lead to the most accurate and optimal outcome.

Question 49

What is the fundamental distinction between deterministic and stochastic models?

Accepted Answer

Deterministic models assume certainty, while stochastic models account for uncertainty.

Answer

Stochastic models are exclusively employed for intricate and uncertain decisions.

Answer

Deterministic models are inherently more accurate than stochastic models due to their simplicity.

Question 50

Which of the following best describes a limitation of using Monte Carlo simulations?

Accepted Answer

They can be computationally demanding, especially for large or complex models.

Answer

They necessitate an extensive amount of historical data to generate meaningful results.

Answer

They consistently yield the most precise and reliable outcomes.

Answer

They are exclusively applicable to simple and straightforward decision problems.

Question 51

What is the primary purpose of conducting sensitivity analysis?

Accepted Answer

To evaluate how variations in input values impact the model's output.

Answer

To determine the most influential input variables in the model.

Answer

To identify the optimal solution to the decision problem at hand.

Question 52

Identify the statement that does NOT describe a characteristic of a well-crafted MCQ.

Accepted Answer

Ambiguous distractors

Answer

Clear and concise question stem

Answer

Plausible distractors

Question 53

A company is considering a new project with an initial investment of $100,000. The project is estimated to generate annual cash flows of $20,000 for the next 10 years. Assuming the company's cost of capital is 5%, calculate the net present value (NPV) of the project.

Accepted Answer

$74,622

Answer

$81,158

Answer

$59,817

Answer

$69,444

Question 54

Consider the normal distribution illustrated below:

![Normal Distribution](https://example.com/normal_distribution.png)

Determine the probability of obtaining a value between -1 and 1 from this distribution.

Accepted Answer

0.6827

Answer

0.3173

Answer

0.9545

Answer

0.7357

Question 55

In a two-person zero-sum game, the payoff matrix contains:

Accepted Answer

The payoffs to player A for each pair of actions

Answer

The probabilities associated with each pair of actions

Answer

The expected payoffs for each player

Question 56

In a linear programming problem, the decision variables represent:

Accepted Answer

The quantities being optimized

Answer

The objective function

Answer

The constraints on the solution

Answer

The coefficients in the inequalities

Question 57

A limitation of using game theory is that it:

Accepted Answer

Assumes rational behavior with complete information

Answer

Can handle complex problems

Answer

Provides optimal solutions

Question 58

In network analysis, a critical path is defined as the:

Accepted Answer

Sequence of activities with the longest duration

Answer

Sequence of activities with the shortest duration

Answer

Sequence of activities with the most dependencies

Question 59

In linear programming, an optimal solution:

Accepted Answer

Maximizes the objective function without violating constraints

Answer

Satisfies all constraints without optimizing the objective function

Answer

Minimizes the objective function while violating some constraints

Question 60

A factory produces two types of products, A and B, using the same machine. Each unit of product A requires 3 hours of machine time, and each unit of product B requires 4 hours of machine time. The factory has 600 hours of machine time available each month. If x represents the number of units of product A and y represents the number of units of product B, which of the following inequalities represents the constraint on the number of units that can be produced?

Accepted Answer

3x + 4y ≤ 600

Answer

4x + 3y ≤ 600

Answer

3x + 4y ≥ 600

Answer

4x + 3y ≥ 600

Question 61

In linear programming, which of the following is the primary goal?

Accepted Answer

To optimize a linear objective function subject to linear constraints.

Answer

To solve a system of linear equations.

Answer

To find the maximum or minimum value of a quadratic function.

Question 62

In a zero-sum game, what is the characteristic of the players' payoffs?

Accepted Answer

They sum to zero.

Answer

They are always negative.

Answer

They are always equal.

Answer

They are always positive.

Question 63

In the context of game theory, what is a Nash equilibrium?

Accepted Answer

A situation where no player can improve their outcome by changing their strategy while the other players' strategies remain unchanged.

Answer

A situation where one player has a dominant strategy.

Answer

A situation where the outcome is always a draw.

Question 64

Which algorithm is primarily used to find the shortest path between two nodes in a weighted, directed graph?

Accepted Answer

Dijkstra's Algorithm

Answer

Kruskal's Algorithm

Answer

Prim's Algorithm

Answer

Floyd-Warshall Algorithm