Q.5. Demand has grown at Dairy May Farms, and it is considering expanding. One option is to expand by purchasing a very large farm that will be able to meet expected future demand. Another option is to expand the current facility by a small amount now and take a wait-and-see attitude, with the possibility of a larger expansion in two years. Management has estimated the following chances for demand: • The likelihood of demand being high is 0.70. • The likelihood of demand being low is 0.30. Profits for each alternative have been estimated as follows: • Large expansion has an estimated profitability of either $40,000 or $20,000, depending on whether demand turns out to be high or low. • Small expansion has a profitability of $15,000, assuming that demand is low. • Small expansion with an occurrence of high demand would require considering whether to expand further. If the company expands at that point, the profitability is expected to be $35,000. If it does not expand further, the profitability is expected to be $12,000. (a) Draw a decision tree showing the decisions, chance events, and their probabilities, as well as the profitability of outcomes. (b) Solve the decision tree you developed. What should Dairy May Farms do?
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- Dairy May Farms has two main decisions: either to undertake a large expansion or a small expansion. - For the large expansion, the profitability depends on demand: - High demand: $40,000 - Low demand: $20,000 - For the small expansion, the profitability also Show more…
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The J.R. Ryland Computer Company is considering a plant expansion to enable the company to begin production of a new computer product. The company's president must determine whether to make the expansion a medium- or large-scale project. Demand for the new product is uncertain, which for planning purposes may be low demand, medium demand, or high demand. The probability estimates for demand are $.20,50,$ and 30 , respectively. Letting $x$ and $y$ indicate the annual profit in thousands of dollars, the firm's planners developed the following profit forecasts for the medium- and large-scale expansion projects. a. Compute the expected value for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of maximizing the expected profit? b. Compute the variance for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of minimizing the risk or uncertainty?
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