Joey Farm is a small, family-operated ranch that sells produce to local markets. The owners are currently trying to decide whether they should expand, keep the same size farm or reduce the size of the farm. They assessed the demand levels for their produce in the local market and probabilities associated with each demand level: high (probability 0.37), medium (probability 0.49), or low (probability 0.14). The payoffs they expect for each demand/acreage scenario are listed below. Acreage Demand Expand Same Size Contract High $115,000 $42,000 $22,000 Medium $43,000 $36,000 $22,000 Low $-18,700 $16,000 $22,000 What is the most money the farm should be paid for information about the demand under these circumstances? Please show your calculations. (4 marks) The farm 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) = 0.69 P(PH\ M) = 0.21 P(PH \ L) = 0.10 P(PM \ H) = 0.19 P(PM \ M) = 0.70 P(PM \ L) = 0.11 P(PL \ H) = 0.12 P(PL \ M) = 0.09 P(PL \ L) = 0.79 Where: H = high demand PH = predict high demand M = medium demand PM = predict medium 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 medium demand.
Joey Farm is a small, family-operated ranch that sells produce to local markets. The owners are currently trying to decide whether they should expand, keep the same size farm or reduce the size of the farm. They assessed the demand levels for their produce in the local market and probabilities associated with each demand level: high (probability 0.37), medium (probability 0.49), or low (probability 0.14). The payoffs they expect for each demand/acreage scenario are listed below.
|
Acreage |
|||
|
Demand |
Expand |
Same Size |
Contract |
|
High |
$115,000 |
$42,000 |
$22,000 |
|
Medium |
$43,000 |
$36,000 |
$22,000 |
|
Low |
$-18,700 |
$16,000 |
$22,000 |
- What is the most money the farm should be paid for information about the demand under these circumstances? Please show your calculations. (4 marks)
- The farm 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) = 0.69 P(PH\ M) = 0.21 P(PH \ L) = 0.10
P(PM \ H) = 0.19 P(PM \ M) = 0.70 P(PM \ L) = 0.11
P(PL \ H) = 0.12 P(PL \ M) = 0.09 P(PL \ L) = 0.79
Where:
H = high demand PH = predict high demand
M = medium demand PM = predict medium 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 medium demand.
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