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 $$000)$ will vary with the amount of precipitation $($rainfall$)$ as follows:

ALTERNATIVE PRECIPITATION

LOW NORMAL HIGH

Do Nothing $-100100300$

Expand $350500200$

Build New $7503000$

If the chances of low, normal, and high precipitation are $30\%,20\%,$ and $50\%,$ respectively, what is the expected value of perfect information?

Multiple Choice

$$285,000$

$$305,000$

$$170,000$

$$475,000$

$$140,000$