Ronald Lau, chief engineer at South Dakota Electronics, has to decide whether to build a new state-of-the-artprocessing facility. If the new facility works, the company could realize a profit of $200,000. If it fails, SouthDakota Electronics could lose $180,000. At this time, Lau estimates a 60% chance that the new process will fail.The other option is to build a pilot plant and then decide whether to build a complete facility. The pilotplant would cost $10,000 to build. Lau estimates a 50-50 chance that the pilot plant will work. If the pilotplant works, there is a 90% probability that the complete plant, if it is built, will also work. If the pilot plantdoes not work, there is only a 20% chance that the complete project (if it is constructed) will work. Laufaces a dilemma. Should he build the plant? Should he build the pilot project and then make a decision?Help Lau by analyzing this problem.