Question

1. Coleman Raphael, chief engineer at Atlantic Chemical, Inc., has to decide whether or not to build a new processing facility using the latest technology. If the new processing facility works, the company could realize a profit of 200,000. If the processing facility fails, the company could lose $150,000. At this time, Coleman estimates there is a 60% chance that the new processing facility will fail.

The other option is to build a pilot plant and then decide whether or not to build a complete facility. The pilot plant will cost $10,000 to build. Coleman estimates there is a 50/50 chance the pilot plant will work. If the pilot plant works, there is a 90% probability that the complete facility, if it is built, will work. If the pilot plant does not work, there is only a 20% chance that the complete facility, if it is constructed, will work. Coleman faces a dilemma. Should he build the new processing facility? Should he build the pilot plant and then make a decision? Help Coleman by analyzing this decision-tree problem.

Answer 1

We will construct decision tree model for a first option where we are not building pilot plant and second option where we are building pilot plant.

Option 1

Option 2- With pilot plant

Now looking at the decision tree models and expected profit for each option. The overall expected profit by constructing pilot plant (Option 2) is higher i.e. $22,500. Hence, the best option for Coleman is to build a pilot plant and then make a decision. With expected profit of $22,500 by building new processing facility it is in favor for Coleman to build new facility once pilot plant is build.