Steve is the director of operations for Diamond Chemical Company. The company is considering whether to launch a new product line, which will require building a new facility. The research required to produce the new product has not been proven to work in a full-scale operation. If Steve decides to build the new facility and the process is successful, Diamond Chemical will earn a profit of

$750,000. If the process is unsuccessful, his company will realize a loss of $900,000. Steve estimates that the probability of the full-scale process succeeding is 65%.

Steve has the option of constructing a pilot plant for

$60,000 to test the new process before deciding to build the full-scale facility. He estimates there is a 58% probability that the pilot plant will prove successful. If the pilot plant succeeds, he thinks the chance of the full-scale facility succeeding is 90%. If the pilot plant fails, he thinks the chance of the full-scale facility succeeding is only 30%.

a. Structure this problem with a decision tree and advise Steve what to do.

b. What is the most Steve should pay to construct the pilot plant?

Note: To solve Problem 17.29, you need to calculate its posterior probabilities. It is an alternative version of Problem 17.28, in which the posterior probabilities were given.

AppendixLO1