The operations manager for a well$-$drilling company must recommend whether to build a new facility, expand his existing one, or do nothing. He estimates that long$-$run profits $($in $$000)$ will vary with the amount of precipitation $($rainfall$)$ as follows: PRECIPITATION ALTERNATIVE LOW NORMAL HIGH Do Nothing $(100)100300$ Expand $350500200$ Build New $7503000$ If he feels the chances of low, normal, and high precipitation are $30$ percent, $20$ percent, and $50$ percent respectively, what is his expected value of perfect information?