Answer
$C^{\prime}(100)=\$ 49.00 $ per item
Work Step by Step
The marginal cost function is the derivative $C^{\prime}$ of the cost function C.
The units of marginal cost are units of cost (dollars, say) per item.
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$C(x)=20,000+50x+\displaystyle \frac{10,000}{x}$
$C(x)=20,000+50x+10,000x^{-1}$
$C^{\prime}(x)=0+50+10000(-x^{-2})$
$=50-10000x^{-2}$
$C^{\prime}(100)=50-10,000(100^{-2})$
$=50-1=49 $ (dollars per item)
$C^{\prime}(100)=\$ 49.00 $ per item
