If $C(x)$ is the cost ef producing $x$ units of a commodity, then the average cest per unt is of $x=\frac{C(x)}{x},$ Consifer she cost fonction $C(x)$ given below. $($Round your answers to the nearest cant.$)$

$C(x)=2,000160x4x^{\frac{3}{2}}$

$($a$)$ Find the total cost $($in dellars$)$ at a production level of $1,000$ units.

$5$

$($b$)$ Find the average cost $($in dollars per unit$)$ at a production level of $1,000$ unis.

$5$ per unit

$($c$)$ Find the marginal cost $($in dottars per unit$)$ at a production level of $1,000$ units.

$5$ per unit

$($d$)$ Find the production level $($in units$)$ that will minimize the average cost.

$$ units

$($e$)$ What is the minimum average cout $($in dollars per unit$)?$

$5$ per unit