1) Oren Joos, an orange farmer in Kern County, California, faces a dilemma. His crop, which has a value of $250,000, is not quite ready for harvest. The weather forecast is for cold weather, and there is a 40% chance that the temperature tonight will be cold enough to freeze and destroy his entire crop, giving him a value of $0. There are two possible actions that he can take to protect his crop if the temperature drops. First, he could set burners in his orange orchard. This would cost $10,000 in gas and overtime labor; in addition, he would suffer a loss of $40,000 to the value of his crop whether or not the temperature drops. Second, (instead of setting burners) he could set up sprinklers to spray the trees. If the temperature drops, the water would freeze on the fruit and provide some insulation. This method is cheaper (it costs $5,000) but less effective. With the sprinklers, the damage to his crop would be to the tune of $100,000 if the temperature drops; there is no damage to the crop if the temperature does not drop. Assume that Oren Joos wants to maximize his expected monetary value.

a) Construct a decision tree describing Oren Joos' decision problem. Clearly indicate the decision nodes, event nodes, probabilities, and monetary outcomes. What is the optimal decision and what is its expected monetary value?

Work for part (a):

ANSWER: ____________________

b) Suppose that Oren could somehow learn before nightfall whether or not the temperature tonight will be cold enough to freeze his crop. Draw a decision tree for this scenario and indicate Oren Joos' optimal decision. What is the expected monetary value of this decision?

Work for part (b):

ANSWER: ____________________

c) What is the most Oren would pay for an accurate weather forecast for tonight?

ANSWER: ____________________