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=-3x^2+155x-1148
Y=-3x^2+155x-1148
2 answers:
Answer:
The maximum amount of profit the company can make is $854.08
Step-by-step explanation:
Let
x ----> the selling price of each widget
y ---> the amount of profit
we have
This is the equation of a vertical parabola open downward (because the leading coefficient is negative)
The vertex represent a maximum
so
The y-coordinate of the vertex represent the maximum amount of profit the company can make
using a graphing tool
Find out the vertex of the quadratic equation
The vertex is the point (25.83,854.08)
see the attached figure
The y-coordinate of the vertex is 854.08
therefore
The maximum amount of profit the company can make is $854.08
You might be interested in
Hey there!
For this, the easiest way to do this is guess+check with some logic behind it. First, we see the equation:
Now to do this, first, we want to see what the ways to break up are. We can make it
or
. We also want to see what ways we can break up 48:
.
From this, we want it so we can multiply these pairs by each other and add them up to equal 28. We already can cross out the first two ways to break up 48 as 48 is greater than 28 already, and though 24 is less, if we were to multiply that by x we would get 24x, and for the remaining 2 it would become 8x (as remember x and 4x are paired, meaning you have to multiply 2 by the other half of the pair, 4x). Adding these gets 32x, which is greater than 28x.
We are left with:
Now, actually, funny thing is all of these happen to work. If you were to multiply 3 by 4x, and 16 by x, you would get 12x+16x=28x. If you were to multiply 4 by 4x, and x by 12, you would also get 12x+16x=28x. Finally, if you were to multiply 6 by 2x and 8 by 2x, you would get 12x+16x=28x. So really here, you can take your pick. let's use 6*8. Writing this out, we get:
(2x+6)(2x+8)
Hope this helps! Sorry that this explanation was actually quite a bad one, if you have any additional questions just ask me.