Problem
A farmer must decide what to do with his land for the next growing season. He can choose to plant corn or soybeans or to not plant anything at all. If he plants nothing at all, the government farm subsidy will pay him $30 per acre.
If the farmer decides to plant corn or soybeans on his land, there is some risk involved. The yield per acre depends on the amount of rainfall. Too much rain or too little rain will give poorer results than the right amount of rainfall. There is a 40 percent probability that the rainfall will be low; there is a 40 percent probability that the rainfall will be medium; and there is a 20 percent chance that the rainfall will be high.
If the farmer decides to plant corn, the yield per acre will be $0, $90, and $50, respectively, if the rainfall is low, medium, or high. If the farmer decides to plant soybeans, the yield per acre will be $40, $70, and $20, respectively, for low, medium, and high amounts of rainfall.
Explain which option should the farmer go for using decision tree analysis.
Draw a proper decision tree using proper notations as explained in lecture and practice exercise and solutions.
Using either word, PowerPoint or excel, draw a decision tree with proper symbols and labels to help you make the decision.