question archive A farming couple have been in the habit of always planting onions on their farm

A farming couple have been in the habit of always planting onions on their farm

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A farming couple have been in the habit of always planting onions on their farm. In previous years, the seeds for the onions 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 insects might destroy some or all of the onion crop. One thing they could do would be to plant a different crop such as carrots which would not be affected by the insects. The carrots would have only a single planting at a cost of $80,000.

This planting would yield a crop in October worth $140,000 if the weather turns out to be good, or $60,000 if the weather turns out to be poor. There is a 70% chance that the weather will be good. If, however, they decide to plant onions, they will have to worry about the insects (but the weather has little effect on the onion crop and can be ignored). The onion crop would cost $100,000 to plant.

There is a 10% chance of a severe infestation of insects, which would destroy the crop, and render any attempt at a second planting in late July not worth doing. A mild infestation (30% chance) would partially destroy the crop, making it worth only $70,000, while having no insects (60% chance) would produce a crop worth $160,000.

After either a mild infestation or no infestation, a second planting could be undertaken, with the same costs and revenues as the first. The probability of a severe, mild, or no infestation would be 25%, 35%, and 40% if the first planting had a mild infestation, but would be 5%, 10%, and 85% if the first planting had no infestation.

Draw the tree, solve it using the rollback procedure, and state the recommendation and the ranking payoff. When drawing the tree, use payoff nodes for intermediate payoffs. 

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