QUESTION 3 A group of engineering professionals is considering the construction of a private school. If the demand is high (i.e., there is a favorable market of the school), the engineers could realise a net profit of R100000. If the market is not favorable, they could lose R40 000. Of course, they do not have to proceed at all, in which case there is no cost. In the absence of any market data, the engineer's best guess is that there is a 50-50 chance the school will be successful. The engineers have been approached by a market research firm that offers to perform a study of the market at a fee of R5 000 . The market researchers have collected the following statements of probability: - Probability of a favorable market given a favorable study =0.82 - Probability of an unfavorable market given a favorable study =0.18 - Probability of a favorable market given an unfavorable study =0.11 - Probability of an unfavorable market given an unfavorable study =0.89 - Probability of a favorable research study =0.55 - Probability of an unfavorable research study =0.45 Draw a decision tree and indicate what the optimal decision will be for the engineers. (18) 4