The Morton Ward Company is considering the introduction of a new product that is believed to have a 50-50 chance ofbeing successful. One option is to try out the product in a test market, at an estimated cost of $2 million, before making theintroduction decision. Past experience shows that ultimately successful products are approved in the test market 80percent of the time, whereas ultimately unsuccessful products are approved in the test market only 25 percent of the time. If the product is successful, the net profit to the company will be $40 million; if unsuccessful, the net loss will be $15million. a. Discarding the test market option, develop a decision analysis formulation of the problem by identifying the decisionalternatives, states of nature, and payoff table. Then apply Bayes’ decision rule to determine the optimal decisionalternative-b. Find the expected value of perfect information. A c. Now including the option of trying out the product in a test market, use TreePlan (and the Excel template for posteriorprobabilities) to construct and solve the decision tree for this problem. A d. Find the expected value of sample information. How large can the cost of trying out the product in a test market beand still be worthwhile to do?