Ronald Lau, chief engineer at Dartmouth Electronics, has to decide Iwhether to build a new state-ottheart processing facility. If the new facility works, the company could realize a profit of $200,000. It it fails, Dartmouth 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 pilot plant would cost$10,000 to build. Lau estimates a 50-50 chance that the pilot plant will work. lithe pilot plant works, there is a 90% probability that the complete plant. it it is built, will also work. lfthe pilot plant does not work. there is only a 20% chance that the complete project (if it is constructed) will work. Lau faces a dilemma. Should he build the plant? Should he build the pilot project and then make a decision? Help Lau by analyzing this problem. The correct decision tree for Ronald is shown in E (all payoffs are in thousands}. FIGURE 1 152 152 W(90%) 190 Build PW(50%) F(10%) Do Not Build - 190 - 10 71 - 114 190 Try Pilot W(20%) Build F(80%) - 190 PF (50% ) - 10 Do Not Build 71 - 10 - 28 W(40%) 200 Build F (60%) - 28 - 180 Decide Now Do Not Build W = Work, F = Fail 0 PW = Pilot Works, PF = Pilot Fails FIGURE 2 152 152 W(90%) 190 Build PW(50%) F(10%) Do Not Build - 190 - 10 71 - 114 190 Try Pilot W(20%) Build F(80%) - 10 - 190 PF (50%) Do Not Build 71 - 10 - 28 W(40%) 200 Build F(60%) 0 - 180 Decide Now Do Not Build W = Work, F = Fail 0 PW = Pilot Works, PF = Pilot FailsFIGURE 3 152 190 152 W(90%) Build PW(50%) F(10%) Do Not Build - 190 - 10 152 - 114 190 Try Pilot W(20%) Build F(80%) PF (50%) 10 190 Do Not Build 152 - 10 - 28 W(40%) 200 Build F(60%) 0 - 180 Decide Now Do Not Build W = Work, F = Fail 0 PW = Pilot Works, PF = Pilot Fails