Chapter 20, Problem 39PS

An entrepreneur wants to determine whether it would be pro�table to establish a gardening service in a local suburb. The entrepreneur believes that there are four possible levels of demand for this gardening service:

Very low demand- $1\%$ of the households would use the service.

Low demand- $5\%$ of the households would use the service.

Moderate demand- $10\%$ of the households would use the service.

High demand- $25\%$ of the households would use the service.

Based on past experiences in other suburbs. the entrepreneur as- signs the following probabilities to the various demand levels:

P(Very low demand) $\text{= 0}\text{.20}$

P(Low demand) = 0.50

P(Moderate demand) $\text{= 0}\text{.20}$

P(High demand) $\text{= 0}\text{.10}$

The entrepreneur has calculated the following pro�ts or losses ($) of this garden service for each demand level (over a period of one year):

a. Construct a decision tree.

b. Construct an opportunity loss table.

c. Compute the expected monetary value (EMV) for offering this garden service.

d. Compute the expected opportunity loss (EOL) for offering this garden service.

e. Explain the meaning of the expected value of perfect information (EVPI) in this problem.

f. Compute the return-to-risk ratio (RTRR) for offering this garden service.

g. Based on the results of (c), (d), and (f), should the entrepreneur offer this garden service? Why?

Before making a �nal decision, the entrepreneur conducts a survey to determine demand for the gardening service. A random sample of 20 households is selected, and 3 indicate that they would use this gardening service.

h. Revise the prior probabilities in light of this sample information.

i. Use the revised probabilities in (h) to repeat (c) through (g).