Question 11

A nuclear power company is deciding whether to build a nuclear plant at Chico Canyon or at Pleasantville. The cost of building the power plant is $14 million at Chico and $20 million at Pleasantville. If the company builds at Chico, however, and an earthquake occurs at Chico during the next 5 years, construction will be terminated and the company will lose $14 million (and will still have to build a power plant at Pleasantville). Without further information, the company believes there is a 20% chance that an earthquake will occur at Chico during the next 5 years.

Suppose that an actual (not perfectly reliable) geologist can be hired to analyze the earthquake risk. The geologist's past record indicates that he will predict an earthquake on 90% of the occasions for which an earthquake will occur and no earthquake on 85% of the occasions for which an earthquake will not occur. Given this information, What is the maximum amount the company can pay the geologist? (answer format as in example 10,000,000)