Marginal Revenue The demand function for a certain boat company's $34$ fit Sundancer yacht is

$p=800-0\mathrm{.}01xln(x)$

where $x$ denotes the number of yachts and $p$ is the price per yacht in hundreds of dollars.

$($a$)$ Find the revenue function $R(x)$ and the marginal revenue function $R(x)$ for this model of yache.

$R(x)=$

$R^2(x)=$

$($b$)$ Use the result of part $($a$)$ to estimate the revenue to be realized from the sale of the ${350}^{th}34$ fi$,$ Sundancer yacht. $($Round your answer to the nearest dollar.$)$

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