# Profit maximization question

I have the following question

A monopolist has a cost function, $\textrm{c}(q)=q$. It faces the following demand function: $$q(p) = \begin{cases} \frac{100}{p} & \textrm{if } p \leq 20 \\ 0 & \textrm{if } p > 20 \end{cases}$$ What are the profit-maximizing price and output?