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

please answer asap!!

Answer 1

Answer:

$x =\ 43.9$

Step-by-step explanation:

The company will break even when it has made no profit, i.e. when $y = 0$:

$y =0 = -x^2+48x-180$.

Using the quadratic formula we get the two solutions:

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

which in decimal form are

$x = \ 4.1$

$x =\ 43.9$

We choose the price $x =\ 43.9$, because it is the highest price for which no profit is made, and higher price means that you could sell least number of products to earn a certain amount of money.

Also. the graph of $y(x)$ relates to the real life situation from the blue line shown in the graph, because what happens in real life is that as you increase the price, your profit decreases.