Question # 2 (8 marks) Vegetables Farm is a small, family-operated ranch that sells produce to local markets. The owners are going to renew their lease and are currently trying to decide whether they should expand their operation upon renewal. Since this is a relatively new business, the owners have assessed the following demand levels and probabilities: high (probability 0.26), medium (probability 0.51), or low (probability 0.23). The payoffs they expect for each demand/acreage scenario are listed below. Lot Size Demand Expand Same Size Contract High $80,000 $49,000 $35,000 Moderate $45,000 $46,000 $35,000 Low $ -25000 $30,000 $35,000 Required: a. A consultant has offered to predict the demand for produce in the local market in the near future for a fee of $4300. Do you believe Vegetable Farm should employ this consultant? Why/Why not? Show your calculations. (4 marks) b. The ranch has hired a consultant to forecast the demand. The consultant has predicted moderate demand. The accuracy of his predictions are as follows: P(PH \ H) = 0.67 P(PH\ M) = 0.22 P(PH \ L) = 0.11 P(PM \ H) = 0.25 P(PM \ M) = 0.72 P(PM \ L) = 0.14 P(PL \ H) = 0.08 P(PL \ M) = 0.06 P(PL \ L) = 0.75 Where H = high demand PH = predict high demand M = moderate demand PM = predict moderate demand L = low demand PL = 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 moderate demand. 4 marks)