To find the maximum amount of profit the company can make, you need to determine the vertex of the quadratic equation in the form y = ax^2 + bx + c, where a = -12, b = 491, and c = -2398.
The x-coordinate of the vertex is given by: x = -b / (2a)
Plugging in the values:
x = -491 / (2 * (-12))
x = 491 / 24
Now, calculate the corresponding y-coordinate of the vertex by substituting this value of x back into the equation:
y = -12x^2 + 491x - 2398
y = -12 * (491/24)^2 + 491 * (491/24) - 2398
Now, calculate y:
y ≈ 5168.33
To the nearest dollar, the maximum amount of profit the company can make is approximately $5,168.