Question

A farmer has been in the habit of always planting potatoes on his farm. In previous years, the seeds for the potatoes were planted in the spring, and were ready to harvest in mid-July. After that, a second planting took place in late July, which was ready to harvest in early October.

This year, however, there is concern that a blight might destroy some or all of the potato crop. One thing he could do would be to plant a different crop such as peas which would not be affected by the blight. The peas would have only a single planting at a cost of $40,000. This planting would yield a crop in October worth $70,000 if the weather turns out to be good, or $30,000 if the weather turns out to be poor. There is a 60% chance that the weather will be good.

If, however, he decides to plant potatoes, he will have to worry about the blight (but the weather has little effect on the potato crop and can be ignored). The potato crop would cost $60,000 to plant. There is a 10% chance of a severe blight, which would destroy the crop, and render any attempt at a second planting in late July not worth doing. A mild blight (20% chance) would partially destroy the crop, making it worth only $35,000, while having no blight (70% chance) would produce a crop worth $80,000. After either a mild blight or no blight, a second planting could be undertaken, with the same costs and revenues as the first. The probability of a severe, mild, or no blight would be 15%, 30%, and 55% if the first planting had a mild blight, but would be 0%, 5%, and 95% if the first planting had no blight.

NOTE: The crop planted in the Spring will be either peas or potatoes; doing a bit of both is not an option in this problem.

Draw the tree, solve it using the rollback procedure, and state the recommen- dation and the ranking payoff. When drawing the tree, use payoff nodes for inter- mediate payoffs.

Please show all workings and show where the numbers come from.

Answer 1

Blight-> Severe, mild, No
Weather-> good, bad
Potatoes aren;t affected by weather conditions and Peas aren't affected by Blight.



Now Lets analyse one after other
(See image uploaded)







Please ask any question which is unclear.(I have spent 1 hour on this solution)