# Using a Decision Tree and finding expected value

Rob Johnson is a product manager at Diamond Chemicals, which is considering whether to launch a new product line that will require it to build a new facility. The technology required to produce the new product is yet untested. If Rob decides to build the new facility and the process is successful, Diamond Chemicals will realize a profit of $650,000. If the process does not succeed, the company will lose $800,000. Rob estimates that there is 60% probability that the process will succeed.

Rob can also decide to build a pilot plant for $50,000 to test the new process before deciding to build the full-scale facility. If the pilot plant succeeds, Rob feels there is 85% chance of the success of the full-scale facility. If the pilot plant fails, Rob feels there is only 20% chance of the success of the full-scale facility. The probability that the pilot plant will succeed is approximately 60%. Structure this problem using a decision tree and advise Rob what to do.

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#### Solution Preview

Option 1

Success (.6)(650,000) = 390,000

Failure (.4)(-800,000) = -320,000 Combining these results gives an expected value of 70,000

Option 2 with pilot plant

Pilot Success and product success (-50,000) + (.60)(.85)(650,000) = 281,500

Pilot Success and product failure ...