A small bakery makes a profit $P\left(c\right)$ in dollars from selling $c$ cakes per day according to the formula $P\left(c\right)=c(40-c)-80$. Considering that $P$ is a continuous function, how many cakes should the bakery sell per day to maximize its profit?

The bakery should sell $10$ cakes per day to maximize its profit.

The bakery should sell $20$ cakes per day to maximize its profit.

The bakery should sell $30$ cakes per day to maximize its profit.

The bakery should sell $40$ cakes per day to maximize its profit.