A2 a A farmer is considering three types of crops to plant f

A2. (a) A farmer is considering three types of crops to plant for next year. Depending on the climate, the profit gained might vary for each type of crops. The payoff table is given as follow State of Climate Crops S1 C1 50 30 45 S2 75 -50 50 50 120 60 2 It is assumed that the probabilities of s1, S2, and s3 are 25%, 35%, and 40%, respectively. Determine the best crop to plant for next year using the following decision criteria (i) Maxmin payoff approach. [10 marks] (ii) Maximum likelihood approach. [10 marks] (ii) What choice should be made under the expectation maximisation approach? [10 marks]

Solution

Profit payoff Prob 0.25 0.35 0.4 Crops S1 S2 S3 Expectation C1 50 75 50 58.75 Best option C1 Ans iii C2 30 -50 120 38 C3 45 50 60 52.75 Profit payoff Prob 0.25 0.35 0.4 Step 1 Step 2 Crops S1 S2 S3 Min Max of Mins C1 50 75 50 50 50 Best option C1 Ans i C2 30 -50 120 -50 C3 45 50 60 45 Profit payoff Max Likely Prob 0.25 0.35 0.4 Crops S1 S2 S3 C1 50 75 50 C2 30 -50 120 Best option C2 Ans ii C3 45 50 60