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Note: This problem requires the calculation of posterior probabilities. Dawson's is a fruit and ...
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Note: This problem requires the calculation of posterior probabilities. Dawson's is a fruit and ...
Note: This problem requires the calculation of posterior probabilities. Dawson's is a fruit and vegetable stand in southern New Jersey that is considering an expansion of the facility to take advantage of increased future demand. The future demand for the business will be strong or weak with a 50/50 chance of each. The following decision table summarizes Dawson's options and the associated payoffs.
Dawson's has the option to hire a market research firm to conduct a survey to better ascertain the demand for their business. The cost of the survey is $5,000. If the market has strong demand for the business, the probability that the survey will predict a strong demand is 76%. If the market has a weak demand for the product, the probability that the survey will predict a strong demand is 32%.
A) Construct a decision tree to determine Dawson's course of action.
B) What is the most that Dawson's should pay for the survey?
Textbook
Business Statistics
Edition:
2
^{nd}
Author:
Donnelly
Read 28 times
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More questions for this book are
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A)
Define the following events:
SS
= survey predicts a strong market
WS
= survey predicts a weak market
SD
= strong demand for product
WD
= weak demand for product
Posterior Probabilities for a Survey that Predicts a Strong Demand
Posterior Probabilities for a Survey that Predicts a Weak Demand
P
(
SD

SS
) =
= 0.70
P
(
WD

SS
) =
= 0.30
P
(
SD

WS
) =
= 0.26
P
(
WD

WS
) =
= 0.70
EMV
_{2}
= (0.7)($125,000) + (0.3)($36,000) = $76,700
EMV
_{3}
= (0.7)($72,000) + (0.3)($36,000) = $55,800
EMV
_{4}
= (0.26)($125,000) + (0.74)($18,000) = $5,860
EMV
_{5}
= (0.26)($72,000) + (0.74)($18,000) = $32,040
EMV
_{1}
= (0.54)($76,700) + (0.46)($32,040) = $56,156.40
EMV
_{6}
= (0.5)($125,000) + (0.5)($36,000) = $44,500
EMV
_{7}
= (0.5)($72,000) + (0.5)($18,000) = $45,000
Final
EMV
= $56,156.40  $5,000 = $51,156.40
B)
The most that Dawson should pay for the survey is $56,156.40  $45,000 = $11,156.40
1
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