Marginal cost and the cost of the next unit

Statement

The total cost is $C(q)=0{.}1q^{2}+15q+400$ (in €). Compute the marginal cost at $q=50$ and interpret it: roughly how much does producing the $51^{\mathrm{st}}$ unit cost?

Solution

$MC(q)=C'(q)=0{.}2q+15$. $MC(50)=0{.}2\cdot 50+15=\boxed{25\ \text{€}}.$ Marginal cost approximates the cost of the next unit: producing the $51^{\mathrm{st}}$ unit costs about $25\ \text{€}$.