An orange grower in Florida faces a dilemma. The weather forecast is for cold we

Question

An orange grower in Florida faces a dilemma. The weather forecast is for cold weather, and there is a 50% chance that the temperature tonight will be cold enough to freeze and destroy his entire crop, which is worth some $50,000. He can take two possible actions to try to alleviate his loss if the temperature drops. First, he could set burners in the orchard; this would cost $5,000, but he could still expect to incur damage of approximately $15,000 to $20,000. The estimated loss is $17,500. Second, 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. The cost is $2,000, but it is less effective. With the sprinklers, he could expect to incur as much as $25,000 to $30,000 of the loss with no protective action.

Compare the grower's expected values for the three alternative he has, considering the various possile loss scenarios for the burners and the sprinklers. Which alternative would you suggest the grower take? Why?

Explanation / Answer

If rain takes place possible losses are as below .

With no protection : 50000$ loss

With burner installed estimated loss is : 17500 $ + 5000 $ capital total loss : 22500 $

With sprinkler installed estimated loss : 27000$ + 2000$ capital cost

Total cost : 29000$

Hence most optimal option is burner installed as it is most otimal solution.

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