Question

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.

y, equals, minus, 12, x, squared, plus, 491, x, minus, 2398
y=−12x
2
+491x−2398

Answer 1

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.