Problem 3 [40 points]: The SweetTooth Candy Company knows it will need 10 tons of sugar six months from now to implement its production plans. The company has essentially two options for acquiring the needed sugar. It can either buy the sugar at the going market price when it is needed, six months from now, or it can buy a futures contract now. The contract guarantees delivery of the sugar in six months but the cost of purchasing it will be based on today's market price. Assume that possible sugar futures contracts available for purchase are five tons or ten tons only. No futures contracts can be purchased or sold in the intervening months. Thus, Sweet Tooths possible decisions are to (1) purchase a futures contract for ten tons of sugar now, (2) purchase a futures contract for five tons of sugar now and purchase five tons of sugar in six months, or (3) purchase all ten tons of needed sugar in six months. The price of sugar bought now for delivery in six months is $0.0851 per pound. The transaction costs for five-ton and ten-ton futures contracts are $65 and $110, respectively. Finally, the company has assessed the probability distribution for the possible prices of sugar six months from now as follows: Price (per pound) $0.078 $0.083 $0.087 $0.091 $0.096 Probability 0.05 0.25 0.35 0.2 0.15 a) Draw a decision tree manually or by PrecisionTree to find the company's optimal decision that minimizes the expected cost of meeting its sugar demand. [25 points] b) Perform a sensitivity analysis manually or by PrecisionTree on the company's optimal decision, by letting each of the three currency inputs (i.e., $0.0851, $65, and $110) vary one at a time plus or minus 25% from its base value, and summarize your findings. In particular, which of the inputs has the largest effect on the company's optimal decision? [15 points)