Question

Steve is the director of operations for a diamond 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, the company will earn a profit of 720,000. 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 62%. Steve has the option of constructing a pilot plant for 59,000 to test the new process before deciding to build the​ full-scale facility. He estimates there is a 54% probability that the pilot plant will prove successful. If the pilot plant succeeds he thinks the chance of the full scale facility succeeding is 87%. if the pilot plant fails, he thinks the chance of the full scale facility succeeding is only 35%. Complete parts a, b, and c below.

A.) Construct a decision tree with all of the known information labeled

B.) Advise what to do ( should he build the pilot plant first?)

C.) what is the most they should pay to construct the pilot plant?

Answer 1

Here we are given with the information that to launch new product, system will require new facility.

We are given with

P(New facility works) = 0.62 and P(New facility fails) = 0.38

P( Pilot plant will work) = 0.54 and P( Pilot plant will fail) = 0.46

We are also given with some conditional probability of success and failure of pilot plant got given facility

P(Pilot plant works | new facility works) = 0.87

P(Pilot plant works | new facility fails) = 0.13

P(Pilot plant fails | new facility works) = 0.35

P(Pilot plant fails| new facility fails) = 0.65

A) We will obtained decision tree with help of given information.

B)

If we build New facility without pilot plant then expected profit is $104400.

So we will advise to build pilot plant. because

If we do pilot plant and it fails then we need not to build new facility.

If we do pilot plant and it succeed then we will build new facility with expected profit as $216076.

C) They should pay $216076 to construct pilot plant.