John Thompson is the founder and president of Thompson Lumber Company, a profitable company located in Toronto ON. John Thompson wants to expand his product line by manufacturing and marketing a new product, backyard storage sheds. To do that he considers two projects. Construct: a. a large new plant to manufacture the storage sheds, b. a small plant, or c. no plant at all (i.e., he has the option of not developing the new product line). Thompson determines that there are only two possible outcomes: the market for the storage sheds could be favorable, meaning that there is a high demand for the product, or it could be unfavorable, meaning that there is a low demand for the sheds. Because Thompson wants to maximize his profits, he can use profit to evaluate each consequence. John Thompson has already evaluated the potential profits associated with the various outcomes. With a favorable market, he thinks a large facility would result in a net profit of $200,000 to his firm. This $200,000 is a conditional value because Thompson's receiving the money is conditional upon both his building a large factory and having a good market. The conditional value if the market is unfavorable would be an $180,000 net loss. A small plant would result in a net profit of $100,000 in a favorable market, but a net loss of $20,000 would occur if the market was unfavorable. Finally, doing nothing would result in $0 profit in either market. Suppose that John Thompson believes that the probability of a favorable market is exactly the same as the probability of an unfavorable market; that is, each state of nature has a 0.50 probability. (a) Develop a decision tree of this problem. (b) What is the best solution? ( Which alternative would give the greatest expected monetary value? )