The operations manager for a well$-$drilling company must recommend whether to build a new facility, expand his existing one, or do nothing. The manager estimates that long$-$run profits $($in $\backslash (\backslash$$ $000\backslash ))$ will vary with the amount of precipitation $($rainfall$)$ as follows: If the chances of low, normal, and high precipitation are $\backslash (30\backslash \%,20\backslash \%\backslash ),$ and $\backslash (50\backslash \%\backslash ),$ respectively, what is the expected value of perfect information? Select one: a$.\backslash (\backslash$$ $285,000\backslash )$ b$.\backslash (\backslash$$ $305,000\backslash )$ c$.\backslash (\backslash$$ $475,000\backslash )$ d$.\backslash (\backslash$$ $140,000\backslash )$ e$.\backslash (\backslash$$ $170,000\backslash )$