Decision Analysis

1)  Given the following payoff matrix:
 


p
Process A
Process B
Process C
Process D
Poor Demand
.3
10
-10
-10
-20
Fair Demand
.5
300
250
350
350
Good Demand
.2
400
450
400
400
a)  What is the Maximin choice and payoff?
b)  What is the Maximax choice and payoff?
c)  What is the Maximum Likelihood choice and payoff?
d)  What is the Bayes (EMV) choice and payoff?
e)  What is the expected value of perfect information?
 f)  Are there any inadmissable acts?  If so, which?


2)  Given the following payoff matrix:
 

 
p
A1
A2
A3
A4
A5
E1
.1
80
70
-20
40
50
E2
.3
-30
90
60
-10
0
E3
.4
70
-10
80
70
70
E4
.2
20
10
30
50
50
a)  What is the Maximin choice and payoff?
b)  What is the Maximax choice and payoff?
c)  What is the Maximum Likelihood choice and payoff?
d)  What is the Bayes (EMV) choice and payoff?
e)  What is the expected value of perfect information?
f)  Are there any inadmissable acts?  If so, which?
 
3)  Bill has decided that despite the volatile economy, after graduating from CSUH, he will follow his dream to open a comic book store.  However, he is undecided as to whether to open a large emporium or a small shop.  In a good economy he expects that a large shop will earn $60,000 in profit, while a small store will command only $30,000 in profit.  Yet, in a poor economy he calculates he would lose $40,000 in a large boutique, while limiting his losses to $10,000 with a small retail outlet. 

Currently, although he is determined to establish himself as a small business owner, he has no idea of which kind of economy to expect.  In a recent conversation one of his old professors offered to custom-build an economic forecasting model for $5,000 to aid Bill in his decision.  The professor indicated that four times out of ten the model would predict a good economy for the shop.  Furthermore, he added that a favorable forecast would indicate a 90% chance of an actual good economy, while an unfavorable result would show a probability of 0.80 of a poor economy occurring.

What should Bill do, and what is the expected value of his decision?
4)  Buzzy-B Toys must decide the course of action to follow in promoting a new whistling yo-yo.  Management must decide whether to market the yo-yo in a national campaign.  In addition, management must decide whether to conduct a test marketing program separate from the national campaign. 

A national success will increase profits by $500,000, and a failure will reduce profits by $100,000.  However, abandoning the product will not affect profits.  The test marketing will cost Buzzy-B $30,000.  If no test marketing is conducted, the probability for a national success is judged to be .45.  The assumed probability for a favorable test marketing result is unknown.  The conditional probability for national success given favorable test marketing is .80; for national success given unfavorable test results the probability is .10.  The company has the option of reengineering the product at a cost of $50,000 given an unfavorable test result.  This process would increase the probability of national success to .35. 

Construct the decision tree diagram and perform backward induction analysis to determine the optimal course of action if an increase in profits is the desired outcome.  What is the optimal decision and the expected value of that decision?

Answers

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