$3\mathrm{.}37$ The physicians in Problem $3-36$ have been approached by a market research firm that offers to perform a study of the market at a fee of $$5,000.$ The market researchers claim their experience enables them to use Bayes$$ Theorem to make the following statements of probability: Condition Probability Favorable market given a favorable study $0\mathrm{.}82$ Unfavorable market given a favorable study $0\mathrm{.}18$ Favorable market given an unfavorable study $0\mathrm{.}11$ Unfavorable market given an unfavorable study $0\mathrm{.}89$ Favorable research study $0\mathrm{.}55$ Unfavorable research study $0\mathrm{.}45$ a$.$ Develop a new decision tree for the medical professionals to reflect the options now open with the market study. b$.$ Use the EMV approach to recommend a strategy. c$.$ What is the expected value of sample information? How much might the physicians be willing to pay for a market study? d$.$ Calculate the efficiency of this sample information