The demand function for a certain commodity is given by $f(x)=250e^{-\frac{x}{1000}},$ where $x$ is the number of items and $f(x)$ is in dollars.

$($a$)$ According to the demand function, what should the price be if one thousand items are available?

$($b$)$ What is the company's revenue under price discrimination if $1000$ items are available?

$($c$)$ What is the consumers' surplus at sales level $x=1000?$