The marginal revenue $($in thousands of dollars$)$ from the sale of $x$ gadgets is given by the following function. The revenue

from $115$ gadgets is $$45,581.$

$MR(x)=4x(x^2+27,000{)}^{-\frac{2}{3}}$

$($a$)$ Find the revenue function.

$($b$)$ What is the revenue from selling $250$ gadgets?

$($c$)$ How many gadgets must be sold for a revenue of at least $$50,000?$