a. Develop a new decision tree for RCI to reflect the options now open with the market study. **Racquet Centers, Inc. (RCI)** is a small investment company considering the construction of a new racquet center. If the demand for the center is high (favorable market), RCI stands to earn a net profit of $100,000. Conversely, if the market is not favorable, the company could incur a loss of $40,000. Alternatively, RCI has the option not to proceed at all, resulting in no cost. Given the lack of any market data, the company currently assumes a 50-50 chance of market success. The critical question is: **What should RCI do?**### Decision TableThe table below outlines the expected monetary values (EMVs) for the decision-making scenario:| Probabilities | 0.5 (Favorable) | 0.5 (Unfavorable) ||--------------------------------------|------------------|--------------------|| **Construct The Center** | $100,000.00 | ($40,000.00) || **Do Nothing** | 0 | 0 |- **EMV of Constructing the Center**: \$30,000.00- **EMV of Doing Nothing**: \$0.00Conclusion: **Obviously, they should construct the center as the table shows the expected monetary value of constructing the center is $30,000.**### Market Research InformationRCI has consulted a market research firm for additional insights. The firm's experience allows them to provide the following **posterior probabilities**:- Probability of a favorable market given a favorable study: **0.82**- Probability of an unfavorable market given a favorable study: **0.18**- Probability of a favorable market given an unfavorable study: **0.11**- Probability of an unfavorable market given an unfavorable study: **0.89**- Probability of a favorable research study: **0.55**- Probability of an unfavorable research study: **0.45**These data points are intended to offer more informed decision-making regarding the potential success of the racquet center.

A decision tree is a graphical representation of possible outcomes based on different decisions.

Racquet Centers, Inc. (RCI) is a small investment company. The company is considering building a new racquet center. If the demand for the center is high (i.e., there is a favorable market for the racquet center), RCI could realize a net profit of $100,000. If the market is not favorable, RCI could lose $40,000. Of course, they don't have to proceed at all; in which case, there is no cost. In the absence of any market data, the best RCI can guess is that there is a 50-50 chance the center will be successful. What should RCI do? Obviously they should construct the center as the following table shows the Expected Monetary value of construction the center is $30,000 Probabilities 0.5 0.5 Favorable Market Unfavorable Market Construct The Center Do Nothing $100,000.00 0 ($40,000.00) 0 EMV= EMV= $30,000.00 $0.00

Racquet Centers, Inc. (RCI) is a small investment company. The company is considering building a new racquet center. If the demand for the center is high (i.e., there is a favorable market for the racquet center), RCI could realize a net profit of $100,000. If the market is not favorable, RCI could lose $40,000. Of course, they don't have to proceed at all; in which case, there is no cost. In the absence of any market data, the best RCI can guess is that there is a 50-50 chance the center will be successful. What should RCI do? Obviously they should construct the center as the following table shows the Expected Monetary value of construction the center is $30,000 Probabilities 0.5 0.5 Favorable Market Unfavorable Market Construct The Center Do Nothing $100,000.00 0 ($40,000.00) 0 EMV= EMV= $30,000.00 $0.00

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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