The Nice Food Production Company (NFPC) is considering producing school meals in the hope of selling it to the Department of Education (DoE) for distribution to schools. The DoE may decide to reject the offer, but it may also decide to purchase the license from NFPC to produce the school meals for either one or two years. At this point in time, NFPC may either start producing the school meals and wait for the DoE decision or transfer the rights for the school meal production to a competitor for 200,000. the food company's decision alternatives and profits (in 000's of 's) are shown in the table below: The probabilities for the states of nature are P(s1)=0.28,P(s2)=0.42, and P(s3)=0.30. For a consulting fee of 25,000, a food agency will review the plans for the school meal offer and indicate the overall chances of a favourable DoE reaction to the proposed offer. Assume that the food agency review will result in a favourable (F) or an unfavourable (U) review and that the following probabilities are relevant: P(F)=0.42P(U)=0.58P(s1F)=0.15P(s2F)=0.55P(s3F)=0.30P(s1U)=0.30P(s2U)=0.25P(s3U)=0.45 (a) Compute the joint probabilities P(Fsk) and P(Usk) for k=1,2,3. (b) Construct a decision tree for this problem. (c) Determine the recommended decision if the agency opinion is not used, and compute the expected value. (d) Compute the expected value of perfect information. (e) What is the optimal decision strategy assuming the agency's information is used? (f) Compute the expected value of the agency's information. (g) Discuss whether the agency's information is worth the 25,000 fee and determine the maximum that the food company should be willing to pay for the information. (h) (i) What is the recommended decision? (ii) Show a risk profile for your recommended decision. (iii) Would you conclude that the review was worth the effort? Justify your reason