Question $2-(40$ points$)$ 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 the 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 $$20,000,$ but he could still expect to incur damage of approximately $$5,000-$$$20,000.$ 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 $($$$17,500),$ but less effective. With

sprinklers he could expect to incur as much as $$10,000$ to $$25,000$ of the loss with no protective

cation.

Using a two$-$way sensitivity analysis, determine the optimal course of action for the grower from

among the three alternatives he has $($including $"$no action" alternative$).$