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 how much the widgets would have to be sold for, to the nearest cent, in order for the company to break even. Only enter one possible price. y=-x^2+48x-180 y=−x 2 +48x−180

Answer 1

Answer:

43.9 cents

Explanation:

The break even point is equivalent to find the roots of the equation. Using quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}$

$x = \frac{-48 \pm \sqrt{48^2 -4(-1)(-180)}}{2(-1)}$

$x = \frac{-48 \pm 39.8}{-2}$

$x_1 = \frac{-48 + 39.8}{-2}$

$x_1 = 4.1$

$x_2 = \frac{-48 - 39.8}{-2}$

$x_2 =43.9$

I'm discarding 4.1 cents price for being too low. 43.9 cents seems to me more reasonable.