Using Bayes€™ decision rule, consider the decision analysis problem having the following payoff table (in units of thousands of dollars):

(a) Which alternative should be chosen? What is the resulting expected payoff?
(b) You are offered the opportunity to obtain information which will tell you with certainty whether the first state of nature S1 will occur. What is the maximum amount you should pay for the information? Assuming you will obtain the information, how should this information be used to choose an alternative? What is the resulting expected payoff (excluding the payment)?
(c) Now repeat part (b) if the information offered concerns S2 instead of S1.
(d) Now repeat part (b) if the information offered concerns S3 instead of S1.
(e) Now suppose that the opportunity is offered to provide information which will tell you with certainty which state of nature will occur (perfect information). What is the maximum amount you should pay for the information? Assuming you will obtain the information, how should this information be used to choose an alternative? What is the resulting expected payoff (excluding the payment)?
(f) If you have the opportunity to do some testing that will give you partial additional information (not perfect information) about the state of nature, what is the maximum amount you should consider paying for this information?

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State of Nature S1 S2 S3 Alternative AT Az -100 -10 10 20 10 100 50 60 10 0.2 0.3 0.5 Prior probability