A start-up firm is considering introducing a new consumer electronics product. If the product is introduced and the market is favorable for the product, then the firm will receive a net profit of $1,500,000. If the product is introduced and the market is unfavorable for the product, then the firm will lose $850.000. The firm believes that there is a 65% chance that the market is favorable for this product (a) Use Bayes Rule to determine the optimal decision for whether or not to introduce the product (b) Find the expected value of perfect information (EVPI) for this situation. (c) Develop a graph that plots the expected payoff of introducing the product versus the probability that the market is favorable. (d) Use algebra to determine the crossover points where the alternative selected by Bayes decision rule in part (a) shifts to the other alternative. The firm has the option of paying a consultant $5,000 for a market survey and analyzing the results before deciding whether or not to introduce the product. The survey will either give a positive result or a negative result. Based on past experience, the consultant advises the firm that if the market is indeed favorable for the product, then there is an 80% chance that the survey will give a positive result. Conversely, if the market is unfavorable, then there is a 70% chance that the survey will give a negative result. (e) Based on the information given above, what is the probability that the consultant's survey will give a positive result? (f) Suppose that the consultant's survey gives a positive result. What is the probability that market is favorable for the product? (g) Suppose that the consultant's survey gives a negative result. What is the probability that market is favorable for the product? (h) Use the Excel template for posterior probabilities to check your answers to parts (e), (f), and (g) (i) Calculate the expected value of experimentation (EVE) in this situation and use it deter- mine whether or not the firm should hire the consultant to conduct the survey