Consider the decision analysis problem with the following payoff table (in units of thou- sands of dollars): State of Nature Alternative S S2 S3 A1 -100 10 100 A2 -10 20 A3 10 10 60 Prior Probability 0.2 0.3 0.5 50 (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 cer- tainty whether the first state of nature S, will occur. What is the maximum amount you should pay for the information? Assuming you will obtain the information, how should it be used to choose an alternative? What is the resulting expected payoff (excluding the payment)? (c) You are offered the opportunity to obtain information which asserts the true state of nature with an accuracy of 60% and wrongly identifies one of the other possible states of nature in 20% of cases each. What is the maximum amount you should pay for the information? Assuming you will obtain the information, how should it be used to choose an alternative? What is the resulting expected payoff (excluding the payment)