Farmer McCoy can plant either corn or soybeans. The probabilities that the next harvest prices will go up, stay the same, or go down are .25, .30, and .45, respectively. If the prices go up, the corn crop will net $30,000 and the soybeans will net $10,000. If the prices remain unchanged, McCoy will (barely) break even. But if the prices go down, the corn and soybeans crops will sustain losses of $35,000 and $5000, respectively. The farmer has the additional option of using the land as a grazing range, in which case a payoff of $7500 is guaranteed. The farmer has also secured additional information from a broker regarding the degree of stability of future commodity prices. The broker’s assessment of “favorable” and “unfavorable” is described by the following conditional probabilities: The symbols a1 and a2 represent the “favorable” and “unfavorable” as- sessments, and s1, s2, and s3 represent the “up”, “same”, and “down” changes in future prices. (a) Develop a decision analysis formulation of this problem by identifying the decision alternatives, the state of nature, and the payoff table. (b) Find EVPI for this problem. (c) Develop a probability tree diagram to obtain the posterior probabilities of the two levels of demand for each of the two possible outcomes of the market research. (d) Find EVE. Specify the optimal decision for the problem.