Question

The company sells widgets, and the relationship between the selling price of each widget, x, and the resulting profit, y, is given by the equation y = -8x^2 + 456x - 2704. What price should the widgets be sold for, rounded to the nearest cent, to maximize the company's profit?

A) $28.50
B) $28.75
C) $29.00
D) $29.25

Answer 1

To maximize the company's profit, the widgets should be sold for B) $28.50.

Step-by-step explanation:

To find the price that should be sold for widgets to maximize the company's profit, we need to find the vertex of the quadratic equation y = -8x^2 + 456x - 2704.

The x-coordinate of the vertex, which represents the price, can be found using the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic equation.

In this case, a = -8 and b = 456.

Plugging these values into the formula, we get x = -456 / (2 * -8) = $28.50.

Therefore, the widgets should be sold for $28.50, rounded to the nearest cent, to maximize the company's profit.