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 0.23), medium (probability 0.53), or low (probability 0.24). The payoffs they expect for each demand/acreage scenario are listed below.

Acreage

DemandExpandedSame Size

High$115,000$45,000

Medium$49,000$42,000

Low$-20,000$16,000

Required:

a.Calculate the expected value of perfect information.

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)= 0.65P(PH\ M)=0.21P(PH \ L)= 0.14

P(PM \ H) = 0.25P(PM \ M) = 0.70P(PM \ L) = 0.20

P(PL \ H)= 0.10P(PL \ M)= 0.09P(PL \ L)= 0.66

Where

H = high demandPH = predict high demand

M = medium demandPM = predict medium demand

L = low demandPL = predict low demand

Based on the accuracy of the prediction, calculate the revised probability for each state of nature (using 3 decimal places at each stage of your calculation) given that the consultant forecast medium demand.