## Consider the pay-off table below, with three alternatives Aj and three states of nature Sj in \$. Let P(S1) = 0.30, P(S­2) = 0.50, P(S3) = 0.20. Compute the expected monetary value for each of the alternatives. (Round the final answer to the nearest dollar

### mathematics

##### Description

Assignment #6 (8%)

This assignment relates to the Course Learning Requirements:

CLR5 Apply decision making using Statistical Decision Theory

Objective of this Assignment:

# Instructions:

Use Word or Excel to solve the following exercises. Please show all your work.

1.       (9 points) Consider the pay-off table below, with three alternatives Aj and three states of nature Sj in \$. Let P(S1) = 0.30, P(S­2) = 0.50, P(S3) = 0.20. Compute the expected monetary value for each of the alternatives. (Round the final answer to the nearest dollar.)

 Alternative S1(\$) S2(\$) S3(\$) A­1 50 70 100 A2 90 40 80 A3 70 60 90

2.      (4 points) Consider the pay-off table below, with three alternatives Aj and three states of nature Sj in \$. Let P(S1) = 0.30, P(S2) = 0.50, P(S3) = 0.20. Develop an opportunity loss table. (Round the final answer to the nearest dollar.)

Pay-off Table:

 Alternative S1(\$) S2(\$) S3(\$) A­1 50 70 100 A2 90 40 80 A3 70 60 90

3.      (10 points) Consider the pay-off table below, with three alternatives Aj and three states of nature Sj in \$. Let P(S1) = 0.30, P(S2) = 0.50, P(S3) = 0.20. Compute the expected opportunity losses for each of the alternatives. (Round the final answer to the nearest dollar.)

Pay-off Table:

 Alternative S1(\$) S2(\$) S3(\$) A­1 50 70 100 A2 90 40 80 A3 70 60 90

4.      (14 points) The Wilhelms Cola Company plans to market a new pineapple-flavoured cola this summer. The decision is whether to package the cola in returnable or in non-returnable bottles. Currently, the provincial legislature is considering eliminating non-returnable bottles. Tybo Wilhelms, president of Wilhelms Cola Company, has discussed the problem with his government representative and established the probability to be 0.70 that non-returnable bottles will be eliminated. The table below shows the estimated monthly profits (in thousands of dollars) if the cola is bottled in returnable versus nonreturnable bottles. Of course, if the law is passed and the decision is to bottle the cola in nonreturnable bottles, all profits would be from out-of-province sales.

 Alternative Law is passed (S1) Law is not passed (S2) Returnable Bottle \$80 \$40 Non-returnable Bottle \$25 \$60

a)     Develop an opportunity loss table, and determine the opportunity loss for each decision.  (Round the final answers to nearest dollar) (8 marks)

b)     Compute the expected profit for both bottling decisions. (Round the final answers to nearest 10th.) (6 marks)

5.      (16 points) Blackbeard's Phantom Fireworks is considering two new bottle rockets. The company can add both to the current line, neither, or just one of the two. The success of these products depends on consumers' reactions to the products. These reactions can be summarized as good, P(S1) = 0.30; fair, P(S2) = 0.50; or poor, P(S3) = 0.20. The company's revenues, in thousands of dollars, are estimated in the accompanying pay-off
table:

 Decision S1 S2 S3 Neither \$0 \$0 \$0 Product 1 only \$125 \$65 \$30 Product 2 only \$105 \$60 \$30 Both \$220 \$110 \$40

a)      Compute the expected monetary value for each decision. (Round the final answers to 2 decimal places.) (4 marks)

b)      What decision would you recommend? (1 mark)

c)       Develop an opportunity loss table. (Round the final answers to the nearest whole number.) (4 marks)

d)      Compute the expected opportunity loss for each decision. (Round the final answers to 2 decimal places.) (4 marks)

e)      Compute the expected value of perfect information. (Round the final answer to the nearest whole number.) (3 marks)