45. Given the following sequential decision tree, determine which is the optimal investment, A or B: $300,000 .304 $60,000 .70 $200,000 Investment A (-$70,000) 40 (-$20,000)7K .60 $45,000 $75,000 20 (-$17,000) .80 $60,000 .35 (-$9,000) . .65 $55,000 $80,000 $70,000 $105,000 $40,000 556 Investment B (-$50,000) 3 .30 46. The management of First American Bank was concerned about the potential loss that might occur in the event of a physical catastrophe such as a power failure or a fire. The bank estimated that the loss from one of these incidents could be as much as $100 million, including losses due to inter- rupted service and customer relations. One project the bank is considering is the installation of an emergency power generator at its operations headquarters. The cost of the emergency generator is $800,000, and if it is installed, no losses from this type of incident will be incurred. However, if the generator is not installed, there is a 10% chance that a power outage will occur during the next year. If there is an outage, there is a .05 probability that the resulting losses will be very large, or approximately $80 million in lost earnings. Alternatively, it is estimated that there is a 95 probability of only slight losses of around $1 million. Using decision tree analysis, determine whether the bank should install the new power generator