A company producing steel construction bars uses the function R(x) = -0.06x2+10.2x -50 to model the unit revenue in dollars for producing x bars. For what number of bars is the revenue at a maximum? What is the unit revenue at that level of production?

Question

A company producing steel construction bars uses the function R(x) = -0.06x2+10.2x -50 to model the unit revenue in dollars for producing x bars. For what number of bars is the revenue at a maximum?  What is the unit revenue at that level of production?

whpalmer4 · Answer

$$R(x) = -0.06x^2+10.2x-50$$
That's a parabola, opening downward ($x^2$ has a negative coefficient).
Do you know how to find the vertex of a parabola?

whpalmer4 · Answer

If you have a parabola with equation written in standard form, $y = ax^2 + bx +c$, the vertex is found at $x = -\dfrac{b}{2a}$

Plug that value of $x$ into the formula to find the unit revenue at the maximum (the y-value of the vertex, in other words).

anonymous · Answer

Ok sorry stepped away for a moment, yes I thought that's the formula that I needed to use. Thanks for the help

anonymous · Answer

I got 85 units

whpalmer4 · Answer

Yes, 85 bars is correct. What's the unit revenue at that point?

anonymous · Answer

$811.90

anonymous · Answer

does that sound correct

anonymous · Answer

actually forgot to square 85 so 383.50

whpalmer4 · Answer

383.50 is correct.