=9.20. Management of the Telemore Company is considering developing and marketing a new product. It is estimated to be twice as likely that the product would prove to be successful as unsuccessful. If it were successful, the expected profit would be

$1,500,000. If unsuccessful, the expected loss would be

$1,800,000. A marketing survey can be conducted at a cost of

$100,000 to predict whether the product would be successful.

Past experience with such surveys indicates that successful products have been predicted to be successful 80 percent of the time, whereas unsuccessful products have been predicted to be unsuccessful 70 percent of the time.

a. Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table when the market survey is not conducted.

b. Assuming the market survey is not conducted, use Bayes’ decision rule to determine which decision alternative should be chosen.