A water supply company is deciding whether or not to build a power plant at Mesa Canyon or at Amherst City. The cost of

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A water supply company is deciding whether or not to build a
power plant at Mesa Canyon or at Amherst City. The cost of building
the power plant is $18 million at Mesa and $32 million at Amherst
City. If the company builds at Mesa, however, and an earthquake
occurs at Mesa during the next five years, construction will be
terminated and the company will lose the $18 million (and will
still have to build a power plant at Amherst City). A priori, the
company believes there is a 20% chance that an earthquake will
occur at Mesa during the next five years. For $500,000, a geologist
can be hired to analyze the fault structure at Mesa Canyon. He will
either predict that an earthquake will occur or that an earthquake
will nto occur. The geologist’s past record indicates that he will
predict an earthquake on 80% of the occasions for which an
earthquake will occur and no earthquake on 80% of the occasions for
which an earthquake will not occur.
a) Draw the decision tree that could be used to solve this
problem, clearly showing all data used in it and state the optimal
policy including the expected payoff.
b) What is the difference in the expected payoff if the
geologist is consulted or not?