During the development of a system under contract, you realize you will not meet two secondary requirements. The customer is not happy about that and is not willing to accept the deviations. Historically, 45% of this type of deviations has been finally accepted by the customer with no penalties, 30% of the projects with a penalty of $100,000, and the rest of the projects with $180,000. The maximum penalties in this project are $250,000, and $100,000 have already been applied to the project. The project manager identifies three alternatives. The first alternative is to not attempt to resolve the deviation and simply accept the penalty. The second alternative is to invest $20,000 in trying to resolve the deviations. The third alternative is to invest first $5,000 in a preliminary analysis and then decide how to continue, depending on the intermediate results. 75.5% of recovery efforts are successful. Out of the successful ones, 55.6% are achieved after investing $20,000 and 26.5% are achieved after investing $30,000. Overall, the company invests $20,000 in recovery actions in 60% of the situations and $30,000 in 25 of the situations. In addition, your team believes with 65% confidence that the $5,000 preliminary analysis will provide promising results. If promising results are found, your team believes that the deviations could be recovered with 80% confidence if investing $15,000. If results are not promising, the team believes that an additional investment of $15,000 might recover the deviation with just 15% confidence. a) Given this information, what is your recommendation to proceed? b) The project manager asks for potentially purchasing clairvoyance for customer acceptance given that the deviation is not recovered before making the investment decision. Please, determine the maximum amount that should be invested in such an effort. c) Please, explain the practical meaning of clairvoyance for b). What would it represent in the actual project? How could clairvoyance (approximately) be acquired in such a realistic scenario? d) Assume the current contingency budget for the project is $120,000 and that the decision-maker is risk-neutral otherwise. Create a utility function and re-evaluate the decision in a).