Price and Revenue

A juice stall sells $120-10p$ cups a day when a cup costs p dollars. Revenue is the money taken: the price times the number sold. So $R\left(p\right) = p\left(120-10p\right)$.

Raising the price is a trade. Each cup earns more, but fewer cups sell. Charge nothing and you earn nothing. Charge 12 dollars and you sell none. Those are the zeros of R, p = 0 and p = 12.

Multiplied out, $R\left(p\right) = -10{p}^{2}+120p$ is a parabola opening down, so the best price is its vertex, halfway between the zeros: 6 dollars. Then $R\left(6\right) = 6\left(60\right)$, which is 360 dollars a day.