Six months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $150 per room. The AMA believes the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of $250 per room. a. Use simulation with @RISK to determine the number of rooms that should be reserved to minimize the expected cost to the AMA. Try possible values from 4100 to 4900 in increments of 100. b. Redo part a for the case where the number attending has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. Does this change the substantive results from part a ?

Question

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Answer 1

Textbook Question

Chapter 10, Problem 29P

Six months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $150 per room. The AMA believes the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of $250 per room.

a. Use simulation with @RISK to determine the number of rooms that should be reserved to minimize the expected cost to the AMA. Try possible values from 4100 to 4900 in increments of 100.
b. Redo part a for the case where the number attending has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. Does this change the substantive results from part a?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

a)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 1

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 2

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 3

Output results:

Run simulation by placing the cursor on B15.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 4

The average cost minimized between 4500 and 4900.

b)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 5

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 6

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 7

Output results:

Run simulation by placing the cursor on B16.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 8

Here, the best number of rooms reserved is somewhat smaller than the numbers in part (a). The average cost is not lower than part (a).

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Answer 2

Textbook Question

Chapter 10, Problem 29P

Six months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $150 per room. The AMA believes the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of $250 per room.

a. Use simulation with @RISK to determine the number of rooms that should be reserved to minimize the expected cost to the AMA. Try possible values from 4100 to 4900 in increments of 100.
b. Redo part a for the case where the number attending has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. Does this change the substantive results from part a?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

a)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 1

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 2

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 3

Output results:

Run simulation by placing the cursor on B15.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 4

The average cost minimized between 4500 and 4900.

b)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 5

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 6

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 7

Output results:

Run simulation by placing the cursor on B16.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 8

Here, the best number of rooms reserved is somewhat smaller than the numbers in part (a). The average cost is not lower than part (a).

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Answer 3

Textbook Question

Chapter 10, Problem 29P

Six months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $150 per room. The AMA believes the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of $250 per room.

a. Use simulation with @RISK to determine the number of rooms that should be reserved to minimize the expected cost to the AMA. Try possible values from 4100 to 4900 in increments of 100.
b. Redo part a for the case where the number attending has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. Does this change the substantive results from part a?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

a)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 1

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 2

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 3

Output results:

Run simulation by placing the cursor on B15.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 4

The average cost minimized between 4500 and 4900.

b)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 5

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 6

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 7

Output results:

Run simulation by placing the cursor on B16.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 8

Here, the best number of rooms reserved is somewhat smaller than the numbers in part (a). The average cost is not lower than part (a).

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 10, Problem 29P

Six months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $150 per room. The AMA believes the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of $250 per room.

a. Use simulation with @RISK to determine the number of rooms that should be reserved to minimize the expected cost to the AMA. Try possible values from 4100 to 4900 in increments of 100.
b. Redo part a for the case where the number attending has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. Does this change the substantive results from part a?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

a)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 1

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 2

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 3

Output results:

Run simulation by placing the cursor on B15.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 4

The average cost minimized between 4500 and 4900.

b)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 5

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 6

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 7

Output results:

Run simulation by placing the cursor on B16.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 8

Here, the best number of rooms reserved is somewhat smaller than the numbers in part (a). The average cost is not lower than part (a).

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 1

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 2

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 3

Output results:

Run simulation by placing the cursor on B15.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 4

The average cost minimized between 4500 and 4900.

b)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 5

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 6

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 7

Output results:

Run simulation by placing the cursor on B16.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 8

Here, the best number of rooms reserved is somewhat smaller than the numbers in part (a). The average cost is not lower than part (a).

Answer 8

a)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 1

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 2

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 3

Output results:

Run simulation by placing the cursor on B15.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 4

The average cost minimized between 4500 and 4900.

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Answer 13

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 1

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 2

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 3

Output results:

Run simulation by placing the cursor on B15.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 4

The average cost minimized between 4500 and 4900.

Answer 14

b)

Expert Solution

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 5

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 6

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 7

Output results:

Run simulation by placing the cursor on B16.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 8

Here, the best number of rooms reserved is somewhat smaller than the numbers in part (a). The average cost is not lower than part (a).

Answer 15

b)

Expert Solution

Answer 16

b)

Expert Solution

Answer 17

Expert Solution

Answer 18

Summary Introduction

To determine: The number of rooms that should be reserved to minimize the expected cost.

Introduction: Simulation model is the digital prototype of the physical model that helps to forecast the performance of the system or model in the real world.

Answer 19

Explanation of Solution

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 5

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 6

Formulae to determine the above table:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 7

Output results:

Run simulation by placing the cursor on B16.

In the @RISK click start simulation to develop the following output results:

Practical Management Science, Chapter 10, Problem 29P , additional homework tip 8

Here, the best number of rooms reserved is somewhat smaller than the numbers in part (a). The average cost is not lower than part (a).

Answer 20

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