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Q5. Vincent Cuomo is the credit manager for the Fine Fabrics Mill. He is currently faced with the question of whether to extend $100,000 credit to a potential new customer, a dress manufacturer. Vincent has three categories for the credit-worthiness of a company: poor risk, average risk, and good risk, but he does not know which category fits this potential customer. Experience indicates that 20 percent of companies similar to this dress manufacturer are poor risks, 50 percent are average risks, and 30 percent are good risks. If credit is extended, the expected profit for poor risks is -$15,000, for average risks $10,000, and for good risks $20,000. If credit is not extended, the dress manufacturer will turn to another mill. Vincent is able to consult a credit-rating organization for a fee of $5,000 per company evaluated. For companies whose actual credit record with the mill turns out to fall into each of the three categories, the following table shows the percentages that were given each of the three possible credit evaluations by the creditrating organization. Actual Credit Record Credit Evaluation Poor Average Good Poor 6 1 1 Average 1 3 0 Good 1 2 a) Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table when the credit-rating organization is not used. b) Assuming the credit-rating organization is not used, use Bayes' decision rule to determine which decision alternative should be chosen (Choose to extend credit with expected payoff $ 8000). c) Find EVPI. Does this answer indicate that consideration should be given to using the credit-rating organization? (EVPI = $3000). d) Assume now that the credit-rating organization is used. Develop a probability tree diagram to find the posterior probabilities of the respective states of nature for each of the three possible credit evaluations of this potential customer. e) Draw and properly label the decision tree. Include all the payoffs but not the probabilities. f) Find the probabilities for the branches emanating from the event nodes. g) Apply the backward induction procedure, and identify the resulting optimal policy. Q5. Vincent Cuomo is the credit manager for the Fine Fabrics Mill. He is currently faced with the question of whether to extend $100,000 credit to a potential new customer, a dress manufacturer. Vincent has three categories for the credit-worthiness of a company: poor risk, average risk, and good risk, but he does not know which category fits this potential customer. Experience indicates that 20 percent of companies similar to this dress manufacturer are poor risks, 50 percent are average risks, and 30 percent are good risks. If credit is extended, the expected profit for poor risks is -$15,000, for average risks $10,000, and for good risks $20,000. If credit is not extended, the dress manufacturer will turn to another mill. Vincent is able to consult a credit-rating organization for a fee of $5,000 per company evaluated. For companies whose actual credit record with the mill turns out to fall into each of the three categories, the following table shows the percentages that were given each of the three possible credit evaluations by the creditrating organization. Actual Credit Record Credit Evaluation Poor Average Good Poor 6 1 1 Average 1 3 0 Good 1 2 a) Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table when the credit-rating organization is not used. b) Assuming the credit-rating organization is not used, use Bayes' decision rule to determine which decision alternative should be chosen (Choose to extend credit with expected payoff $ 8000). c) Find EVPI. Does this answer indicate that consideration should be given to using the credit-rating organization? (EVPI = $3000). d) Assume now that the credit-rating organization is used. Develop a probability tree diagram to find the posterior probabilities of the respective states of nature for each of the three possible credit evaluations of this potential customer. e) Draw and properly label the decision tree. Include all the payoffs but not the probabilities. f) Find the probabilities for the branches emanating from the event nodes. g) Apply the backward induction procedure, and identify the resulting optimal policy

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