1. The electric company is in the process of building a new power plant. There is some uncertainty regarding the size of the plant to be built. If the community that the plant will service attracts a large number of industries, the demand for electricity will be high. If commercial establishments ( offices and retail stores) are attracted, demand will be moderate. If neither industries nor commercial stores locate in the community, the electricity demand will be low. The company can build a small, medium, or large plant, but if the plant is too small, the company will incur extra costs. The total costs ( in $millions) of all options are shown in the accompanying table.
Size of Plant
Electricity Demand Small Medium Large
Low 220 300 350
Moderate 330 320 350
High 440 390 350
The following probabilities are assigned to the electricity demand.
a. Determine the act with the largest expected monetary value. (Caution: All the values in the table are costs).
b. Draw up an opportunity loss table
c. Calculate the expected opportunity loss for each decision and determine the optimal decision.
2. An international manufacturer of electronic products is contemplating introducing a new type of compact disk player. After some analysis of the market, the president of the company concludes that, within 2 years, the new product will have a market share of 5%, 10%, or 15%. She assesses the probabilities of these events as .15,.45, and.40, respectively. The vice president of finance informs her that if the product captures only a 5% market share the company will lose $28 million. A 10% market share will produce a $2-million profit, and 15% market share will produce an $8-million profit. If the company decides not to begin production of the new compact disk player, there will be no profit or loss. Based on the expected decision, what should the company do?
This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Statistics and provides students with a clear perspective of the underlying concepts.