The profit obtained in millions of dollars depends on the selling price in dollars, so the selling price lies on the x-axis, profit lies on the y-axis

The maximum profit can be known by calculating the vertex (h, k) of the given quadratic equation.

h = \frac{-b}{2a} and k = f(h).

The given equation is P = -x^{2} + 12 x + 12. This is as you know is in the standard form y = ax^{2} + bx + c.

So. a = -1, b = 12, c = 12

h = \frac{-12}{-2} = 6.

So, k = -6^{2} + 12 \cdot 6 + 12 = -36 + 72 + 12 = 48

So, the vertex is (6,48). This means that if the selling price is $6 , the profit from the sale of the product was $48

This is the maximum profit, that the company can earn by selling the product.