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Question :
16.The Video Game Supply Company (VGS) deciding whether to set : 1414840

16.The Video Game Supply Company (VGS) is deciding whether to set production next year at 2,000, 2,500, or 3,000 games. Demand could be low, medium, or high. Using historical data, VGS estimates the probabilities as 0.4 for low demand, 0.3 for medium demand, and 0.3 for high demand. The following profit payoff table (in $100s) has been developed.

**Production Target****Low****Quantity Demanded**

**Medium****High**

2,0001,0001,2001,400

2,5008001,5001,300

3,0006001,7001,400

a.Determine the expected value of each alternative and indicate what should be the production target.

b.Determine the expected value with perfect information about the states of nature.

c.Determine the expected value of perfect information.

17.You are given a decision situation with three possible states of nature S_{1}, S_{2}, and S_{3}. The prior probabilities of the three states are 0.20, 0.45, and 0.35. With sample information I, you are provided with the following information.

P(I_{1}?S_{1}) = 0.85P(I_{1}?S_{2}) = 0.70P(I_{1}?S_{3}) = 0.40

a.Compute P(I).

b.Compute the revised probabilities of P(S_{1}?I), P(S_{2}?I), and P(S_{3}?I).

18.Assume you have a sum of money available that you would like to invest in one of the two available investment plans: stocks or bonds. The conditional payoffs of each plan under two possible economic conditions are as follows.

**Economic Condition I****Economic Condition II**

Stocks$40,000$8,000

Bonds$8,000$12,000

a.If the probability of Economic Condition I occurring is 0.8, where should you invest your money? Use the expected monetary value criterion and show your complete work.

b.Compute the expected value with perfect information about the economic conditions (expected value under certainty).

c.Determine expected value of perfect information (EVPI).

19.Consider the following profit payoff table.

**Decision**

**Alternative****States of Nature**

**S**_{1}**S**_{2}

d_{1}86

d_{2}164

What should the probabilities of S1 and S2 be so that the expected monetary values of the two decision alternatives equal one another?

20.Assume you are faced with the following decision alternatives and two states of nature. The payoff table is shown below.

**States of nature 1****States of nature 2**

**Decision Alternatives**0.420.58

**Decision 1**2632

**Decision 2**4018

**Decision 3**2825

The probability of state of nature 1 is P(s_{1}) = 0.42.

a.Determine the expected value of each alternative.

b.Which decision is the optimal decision?

c.Determine the expected value with perfect information.

d.Compute the expected value of perfect information.