Problem 1 The owner of a fruit orchard in the southern US has a decision to make today. The weather forecast for tonight is for cold weather, and there is a good chance that the temperature tonight will be cold enough to freeze, and destroy the entire crop, which is worth $110,000. The owner believes that the probability of a freeze is between 20% and 50%. She has two alternatives to try to reduce this damage if the temperature drops. First, he could set up sprinklers to spray water on the trees. Then if the temperature freczes, the water would frecze on the fruit and provide some insulation. This method costs $6000, and would reduce the losses to between $70,000 and $90,000 Alternatively, she could could set up burners in the orchard, which burn gas and warm up temperatures slightly. This method costs $35,000, but then all damages would be avoided ($0 would occur) if there is a frecze. Show a decision tree for this decision (a) (b) Construct a tornado diagram for the two uncertainties (the probability of a freeze, and amount of damage if sprinklers are used and a freeze occurs). Assume that the nominal orbase case value for the probability is 35% and for the losses for the sprinkler case is 80,000 (when varying one variable from lowest to highest, assume the other variable is at its base case value) (c) Draw a two dimensional diagram showing which alternative is best under all possible combinations of the probability of freeze and the damage if sprinklers are used (i.c., a two way sensitivity analysis, showing the strategy regions, with one axis being the probability and the other being the damage).
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