mathematics help - 35756

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  • Due on: Sat 07 Dec, 2013 (10:53pm)
  • Asked on: Sat 07 Dec, 2013
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Description

An entrepreneur wants to determine whether it would be profitable 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 assigns the following probabilities to the various demand levels:

P(High demand) = 0.10

P(Moderate demand) = 0.20

P(Low demand) = 0.50

P(Very low demand) = 0.20

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

DEMAND

Provide Garden Service

Do Not Provide Garden Service

Very low

-50000

low

60000

Moderate

130000

High

300000

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 final 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. (Hint: Use the binomial distribution to determine the probability of the outcome that occurred, given a particular level of demand.) i. Use the revised probabilities in (h) to repeat (c) through (g).

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