A plant manager wants to know how much he should be willing to pay for perfect market research. Currently there are two states of nature facing his decision to expand or do nothing. Under favorable market conditions the manager would make $$100,000$ for the large plant and $$5,000$ for the small plant. Under unfavorable market conditions the large plant would lose $$50,000$ and the small plant would make $$0.$ If the two states of nature are equally likely, how much should he pay for perfect information?

$$50,000$

$$0$

$$25,000$

$$100,000$

$$145,000$