Operations Research Quiz: Trivia Test!

1. The scientific method in O.R. study generally involves

Judgement Phase

Research Phase

Action Phase

All of the given

None of the given

The correct answer is "All of the given". The scientific method in O.R. study generally involves three phases: the Judgement Phase, the Research Phase, and the Action Phase. In the Judgement Phase, researchers identify the problem and define the objectives. In the Research Phase, they gather relevant data, analyze it, and develop models or theories. In the Action Phase, they implement the solutions and evaluate their effectiveness. Therefore, all three phases are involved in the scientific method in O.R. study.

Explanation

The correct answer is "All of the given". The scientific method in O.R. study generally involves three phases: the Judgement Phase, the Research Phase, and the Action Phase. In the Judgement Phase, researchers identify the problem and define the objectives. In the Research Phase, they gather relevant data, analyze it, and develop models or theories. In the Action Phase, they implement the solutions and evaluate their effectiveness. Therefore, all three phases are involved in the scientific method in O.R. study.

2. In a departmental store, customers arrive at a rate of 20 customers per hour. the average number of customers that can be handled by the cashier is 24 per hour. The probability that the cashier is idle?

1

1/6

5

5/6

The probability that the cashier is idle can be calculated using the concept of the Poisson distribution. The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space. In this case, the arrival rate of customers is given as 20 per hour, and the average number of customers that can be handled by the cashier is 24 per hour.

To find the probability that the cashier is idle, we need to find the probability of having 0 customers arrive in a given hour. This can be calculated using the Poisson distribution formula, where λ (lambda) is the average rate of arrivals.

P(X = 0) = (e^-λ * λ^0) / 0!

Substituting the given values, we have λ = 20 (arrival rate) and e^-λ = e^(-20).

P(X = 0) = (e^-20 * 20^0) / 0!

Simplifying, we get P(X = 0) = e^-20 / 1 = e^-20.

The value of e^-20 is approximately 2.06115e-09.

Therefore, the probability that the cashier is idle is approximately 2.06115e-09 or 1/6.

Explanation

The probability that the cashier is idle can be calculated using the concept of the Poisson distribution. The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space. In this case, the arrival rate of customers is given as 20 per hour, and the average number of customers that can be handled by the cashier is 24 per hour.

To find the probability that the cashier is idle, we need to find the probability of having 0 customers arrive in a given hour. This can be calculated using the Poisson distribution formula, where λ (lambda) is the average rate of arrivals.

P(X = 0) = (e^-λ * λ^0) / 0!

Substituting the given values, we have λ = 20 (arrival rate) and e^-λ = e^(-20).

P(X = 0) = (e^-20 * 20^0) / 0!

Simplifying, we get P(X = 0) = e^-20 / 1 = e^-20.

The value of e^-20 is approximately 2.06115e-09.

Therefore, the probability that the cashier is idle is approximately 2.06115e-09 or 1/6.

3. The North West Corner rule.

Is used to find an initial feasible solution

Is used to find an optimal solution

Is based on the concept of minimizing opportunity cost

None of the given

The North West Corner rule is a method used in transportation problem to find an initial feasible solution. It starts by allocating the maximum possible amount of supply to the first row and first column of the transportation table, and then gradually moves to the next row and column until all supply and demand are satisfied. This method ensures that the initial solution is feasible, meaning that it meets the supply and demand constraints of the problem.

Explanation

The North West Corner rule is a method used in transportation problem to find an initial feasible solution. It starts by allocating the maximum possible amount of supply to the first row and first column of the transportation table, and then gradually moves to the next row and column until all supply and demand are satisfied. This method ensures that the initial solution is feasible, meaning that it meets the supply and demand constraints of the problem.

4. In a departmental store, customers arrive at a rate of 20 customers per hour. the average number of customers that can be handled by the cashier is 24 per hour. What is the arrival rate in this problem?

20

3

24

10

The arrival rate in this problem is 20 customers per hour. This is determined by the given information that customers arrive at a rate of 20 customers per hour.

Explanation

The arrival rate in this problem is 20 customers per hour. This is determined by the given information that customers arrive at a rate of 20 customers per hour.

5. What is meant by 'Payoffs' in Game Theory?

Outcome of a game when different alternatives are adopted by players

No. of players involved in a game

Value of a game

Strategies used by players

Payoffs in Game Theory refer to the outcomes or results of a game when different alternatives are adopted by the players. It represents the benefits or costs that each player receives based on the choices they make. Payoffs can be in the form of monetary rewards, utility, or any other measure of value. They are used to analyze and evaluate the effectiveness of different strategies employed by players in a game and to determine the optimal decision-making process.

Explanation

Payoffs in Game Theory refer to the outcomes or results of a game when different alternatives are adopted by the players. It represents the benefits or costs that each player receives based on the choices they make. Payoffs can be in the form of monetary rewards, utility, or any other measure of value. They are used to analyze and evaluate the effectiveness of different strategies employed by players in a game and to determine the optimal decision-making process.

6. A competitive situation is known as a 'game' if it has given characteristics.

Numbers of players is finite

The players make individual decision without direct communication

The payoff is fixed and determined in advance

All given

None of the given

A competitive situation is considered a 'game' if it satisfies all of the given characteristics. These characteristics include having a finite number of players, individual decision-making without direct communication between players, and a fixed and predetermined payoff. Therefore, all of the given characteristics must be present for a situation to be classified as a 'game'.

Explanation

A competitive situation is considered a 'game' if it satisfies all of the given characteristics. These characteristics include having a finite number of players, individual decision-making without direct communication between players, and a fixed and predetermined payoff. Therefore, all of the given characteristics must be present for a situation to be classified as a 'game'.

7. In a departmental store, customers arrive at a rate of 20 customers per hour. the average number of customers that can be handled by the cashier is 24 per hour. What is the service rate in this problem?

20

3

24

10

The service rate in this problem is 24. This means that on average, the cashier is able to handle 24 customers per hour. Since the arrival rate is also given as 20 customers per hour, it indicates that the service rate is higher than the arrival rate, allowing the cashier to handle all the customers efficiently.

Explanation

The service rate in this problem is 24. This means that on average, the cashier is able to handle 24 customers per hour. Since the arrival rate is also given as 20 customers per hour, it indicates that the service rate is higher than the arrival rate, allowing the cashier to handle all the customers efficiently.

8. Which of the following is not a major requirement of a Linear Programming Problem?

There must be alternative course of action among which to decide

An objective for the firm must exist

The problem must be of maximization type

Resources must be limited

The given answer states that "The problem must be of maximization type" is not a major requirement of a Linear Programming Problem. This means that a Linear Programming Problem does not necessarily have to be a maximization problem, it can also be a minimization problem. Linear Programming can be used to optimize objectives, whether they are to maximize profits or minimize costs. Therefore, the requirement for the problem to be of maximization type is not a major requirement.

Explanation

The given answer states that "The problem must be of maximization type" is not a major requirement of a Linear Programming Problem. This means that a Linear Programming Problem does not necessarily have to be a maximization problem, it can also be a minimization problem. Linear Programming can be used to optimize objectives, whether they are to maximize profits or minimize costs. Therefore, the requirement for the problem to be of maximization type is not a major requirement.

9. Which of the following assertations is true of an optimal solution to an Linear Programming Problem?

Every LP has an optimal solution

The optimal solution always occur at extreme points

If an optimal solution exists, there will always be atleast one at a corner

All of the given

An optimal solution to a linear programming problem refers to the best possible solution that maximizes or minimizes the objective function while satisfying all the constraints. The given answer, "All of the given," suggests that all the assertions mentioned in the options are true for an optimal solution. This means that every LP problem has an optimal solution, the optimal solution always occurs at extreme points, and if an optimal solution exists, there will always be at least one at a corner.

Explanation

An optimal solution to a linear programming problem refers to the best possible solution that maximizes or minimizes the objective function while satisfying all the constraints. The given answer, "All of the given," suggests that all the assertions mentioned in the options are true for an optimal solution. This means that every LP problem has an optimal solution, the optimal solution always occurs at extreme points, and if an optimal solution exists, there will always be at least one at a corner.

10. In Vogel's Approximation Method; the opportunity cost associated with a row is determined by:

The difference between the smallest cost and the next smallest cost in the row

The difference between the smallest unused cost and the next smallest unused cost in the row

The difference between the smallest cost and next smallest unused cost in the row

None of the given

In Vogel's Approximation Method, the opportunity cost associated with a row is determined by the difference between the smallest unused cost and the next smallest unused cost in the row. This means that the method takes into account the costs that have not been assigned to any cell in the row, and calculates the difference between the two smallest unused costs. This approach helps in identifying the row with the highest opportunity cost, which is then used to make the optimal assignment in the transportation problem.

Explanation

In Vogel's Approximation Method, the opportunity cost associated with a row is determined by the difference between the smallest unused cost and the next smallest unused cost in the row. This means that the method takes into account the costs that have not been assigned to any cell in the row, and calculates the difference between the two smallest unused costs. This approach helps in identifying the row with the highest opportunity cost, which is then used to make the optimal assignment in the transportation problem.