While El Ni̱o is pouring its rain on northern California, Charlotte Rothstein, CEO, major shareholder and founder of Cerebrosoft, sits in her office, contemplating the decision she faces regarding her company۪s newest proposed product, Brainet. This has been a particularly difficult decision. Brainet might catch on and sell very well. However, Charlotte is concerned about the risk involved. In this competitive market, marketing Brainet also could lead to substantial losses. Should she go ahead anyway and start the marketing campaign? Or just abandon the product? Or perhaps buy additional marketing research information from a local market research company before deciding whether to launch the product? She has to make a decision very soon and so, as she slowly drinks from her glass of high protein-power multivitamin juice, she reflects on the events of the past few years.
Cerebrosoft was founded by Charlotte and two friends after they had graduated from business school. The company is located in the heart of Silicon Valley. Charlotte and her friends managed to make money in their second year in business and continued to do so every year since. Cerebrosoft was one of the first companies to sell software over the Internet and to develop PC-based software tools for the multimedia sector. Two of the products generate 80 percent of the company€™s revenues: Audiatur and Videatur. Each product has sold more than 100,000 units during the past year. Business is done over the Internet: customers can download a trial version of the software, test it, and if they are satisfied with what they see, they can purchase the product (by using a password that enables them to disable the time counter in the trial version). Both products are priced at $75.95 and are exclusively sold over the Internet.
TABLE 1 Probability distribution of unit sales, given a high price ($50)

TABLE 2 Probability distribution of unit sales, given a medium price ($40)

TABLE 3 Probability distribution of unit sales, given a low price ($30)

(a) For the initial analysis, ignore the opportunity of obtaining more information by hiring the marketing research company. Identify the decision alternatives and the states of nature. Construct the payoff table. Then formulate the decision problem in a decision tree. Clearly distinguish between decision and event nodes and include all the relevant data.
(b) What is Charlotte€™s decision if she uses the maximum likelihood criterion? The maximin payoff criterion?
(c) What is Charlotte€™s decision if she uses Bayes€™ decision rule?
(d) Now consider the possibility of doing the market research. Develop the corresponding decision tree. Calculate the relevant probabilities and analyze the decision tree. Should Cerebrosoft pay the $10,000 for the marketing research? What is the overall optimal policy?

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Level of Competition Sales High Mediumm Low 50,000 units 30,000 units 20,000 units 0.2 0.25 0.55 0.25 0.3 0.45 0.3 0.35 0.35 Level of Competition Sales Mediumm High 0.25 0.35 0.40 Low 50,000 units 30,000 units 20,000 units 0.30 0.40 0.30 0.40 0.50 0.10 Level of Competition Sales High Medium Low 50,000 units 30,000 units 20,000 units 0.35 0.40 0.25 0.40 0.50 0.10 0.50 0.45 0.05