Let's assume that there is a firm that produces a single good, $q=f(x)$, where $x$ is a single input. The firm can sell it on the market at a price $p$. It's production cost is given by a cost function $c(x)$.
In the most microeconomics textbooks the profit maximization problem is expressed as
$maxΠ=max\{pq-c(x)\}$, where $q$ is assumed to be linear function of $x$.
I am wondering if there is a textbook (or a resource in general) in which profit function is expressed as
$Π=pf(x)-c(x)$, where $f$ is concave in $x$ and $c$ is convex in $x$.