Question $1$

$(30$ points$)$ An orange grower 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 $$50,000.$ He can take two possible actions to try to reduce his loss if the temperature drops. First, he could set burners in the orchard; this would cost $$7,000.$ 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 $($ $$2,000),$ but less effective. The loss he will face if he use the burners is uniformly distributed between $$10,000$ and $$20,000.$ Also, the loss incurred with the sprinklers is uniformly distributed between $$20,000$ and $$40,000.$

a$.(5$ points$)$ Draw a decision tree for this problem.

b$.(25$ points$)$ Determine the best alternative by using the Two$-$Bracket Median Method.