A mаnаger оf а new prоductiоn facility is considering to decide whether to open one, two, or three production assembly lines. She estimates that profits next year (in thousands of dollars) will vary with demand for her product and has estimated demand in three categories low, medium and high.Decision AlternativeState of Nature# of production linesDemand is LowDemand is MediumDemand is highOne160280210Two0180230Three-200380980a. If she feels the chances of low, medium, and high demand are 35%, 25%, and 40% respectively, what are the expected annual profits for one beautician she will decide to hire? b. If she feels the chances of low, medium, and high demand are 35%, 25%, and 40% respectively, what are the expected annual profits for two beauticians she will decide to hire? c. If she feels the chances of low, medium, and high demand are 35%, 25%, and 40% respectively, what are the expected annual profits for three beauticians she will decide to hire? d. If she feels the chances of low, medium, and high demand are 35%, 25%, and 40% respectively, what is her expected value of perfect information?
Thоmpsоn Reаl Estаte Cоmpаny in Grand Forks is to consider constructing an apartment complex for renting. There are three alternatives and their payoffs as the table shown. The probabilities of the chance events now are 60 % for favorable market and 40% for unfavorable market. State of Nature Decision AlternativeFavorable Market ($)Unfavorable Market ($) Construct Large complex400,000-360,000 Construct Small complex200,000-50,000 No Plant at all00 Before deciding about building a new complex. The company has the option of conducting a marketing research survey, at a cost of $20,000. The company understands that a market survey will provide sample information, but it may help quite a bit. The market survey will come out either Positive or Negative. Following four conditional probabilities were known.P (survey positive | FM) = 0.7 P (survey negative | FM) = 0.3P (survey positive | UM) = 0.2P (survey negative | UM) = 0.8P (FM) = 0.6P (UM) = 0.4Formula: P (A∩B) = P (B∩A) = P (B) *P (A|B) or P (A) *P (B|A)a. Calculate marginal probability of Survey Positive and Survey Positive? P (survey positive) and P (survey negative).b. Calculate conditional probabilities: P (FM | survey positive) and P (UM | survey positive)c. Calculate conditional probabilities: P (FM | survey negative) and P (UM | survey negative)d. Calculate Expected Value of Sample Information, given EVw/o SI = 100,000