The manager of a large farm devotes the farmland to growing one crop at a time. He now needs
to make a decision on which one of four crops to grow during the upcoming season. The payoff
table for the four crops under various weather conditions with the probabilities are given below.
Decision
State of nature
alternative
Dry Moderate Damp
Crop 1 20.000 35 000 40 000
Crop 2 15 000 20 000 30 000
Crop 3 30.000 25 000 25 000
Crop 4 40 000 40 000 40 000
Probability 0,3 0.5 0,2
3.1 Construct a decision tree for the farm manager's problem, showing the decision alternatives,
the states of nature, the given payoffs and probabilities on the tree.
(8)
3.2 Calculate the expected value (EV) for all five decision nodes.
(5)
3.3 Which crop would you recommend to the manager using the expected value approach? (1)
3.4 Using the conservative approach of maximin, which crop would you recommend the farmer
should grow?
(4)
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