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

$R^{\text{'}}(x)=4x(x^2+26,000{)}^{-\frac{2}{3}}$

$($a$)$ Find the total revenue function if the revenue from $115$ devices is $$13,863.$

$($b$)$ How many devices must be sold for a revenue of at least $$47,000?$

$($a$)$ The total revenue function is $R(x)=,$ given that the revenue from $115$ devices is $$13,863.$

$($Round to the nearest integer as neededn$)$