Answer:
[tex]x =\$43.9[/tex]
Step-by-step explanation:
The company will break even when it has made no profit, i.e. when [tex]y = 0[/tex]:
[tex]y =0 = -x^2+48x-180[/tex].
Using the quadratic formula we get the two solutions:
[tex]x = \dfrac{-48\pm\sqrt{48^2-4(-1)(-180)} }{-2}[/tex]
which in decimal form are
[tex]x = \$4.1[/tex]
[tex]x =\$43.9[/tex]
We choose the price [tex]x =\$43.9[/tex], 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 [tex]y(x)[/tex] 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.
