Vegetables Farm is a small, family-operated ranch that sells produce to local markets. The owners are currently trying to decide whether they should expand their operation next year. Since this is a fairly new business, the owners have assessed the following demand levels and probabilities: high (probability 0.24), medium (probability 0.54), or low (probability 0.22). The payoffs they expect for each demand/acreage scenario are listed below.

Demand

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AcreageHighMediumLow

Expanded$120,000$54,000$-15,050

SameSize50,00047,00021,050

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a.What is the most the ranch should pay for information about the demand. (4 marks)

b.The ranch has hired a consultant to forecast the demand.The consultant has predicted medium demand.The accuracy of his predictions are as follows:

P(PH \ H)=0.67P(PH\ M)=0.22P(PH \ L)= 0.11

P(PM \ H) =0.25P(PM \ M) =0.72P(PM \ L) = 0.14

P(PL \ H)=0.08P(PL \ M)=0.06P(PL \ L)= 0.75

Where:

H = high demandPH = predict high demand

M = mediumdemandPM = predict medium demand

L = lowdemandPL = predict low demand

Based on the accuracy of the prediction, calculate the revised probability for each state of nature (to 3 decimal places) given that the consultant forecast medium demand. (4 marks)

Does your answer to part (a) remain the same in light of the new information?Show your calculations. (2 marks)