A plant manager wants to know how much she should be willing to pay for perfect market research. Currently there are two states of nature facing her decision to expand or do nothing. Under favorable market conditions the manager would make $$180,000$ for the large plant and $$5,000$ for the small plant. Under unfavorable market conditions the large plant would lose $$81,000$ and the small plant would make $$0.$ If the two states of nature are equally likely, how much should she pay for perfect information? $($Round answer to the nearest dollar.$)$

A$.$ $$40,500$

B$.$ $$133,000$

C$.$ $$185,000$

D

E$.$ $$81,000$