Question

R=800x-0.2x^2 find the number of units x that produces a maximum revenue R

Answer 1

Rmax = -800/2*-0.2

Answer 2

yep,
=2000

Answer 3

hey mandolino tell the procedure

Answer 4

yeah thanks for nothin

Answer 5

You have a quadratic function of the form\[y=ax^2+bx+c\]which is maximized at \[x=\frac{-b}{2a}\]This expression comes from the quadratic formula, specifically the ratio of the first term to the denominator. It represents the axis of symmetry for the graphical representation of the function. That is, the expression\[x=\frac{\ \pm\sqrt{b^2-4ac}}{2a}\]is the other part of the quadratic formula, and it is the part that yields the points on either side of the axis of symmetry for the horizontal line y=0.

In your example, you have a=-0.2 and b=800. So the axis of symmetry is\[x=\frac{-800}{-0.2}=2000\]Now we know that this is the location of the maximum because the shape of the quadratic function is a parabola, and when the leading coefficient, a, is negative the parabola opens downward. Technically, we have an x-axis reflection relative to the power function \[f(x)=x^2\]which has leading coefficient a=1, and the parabola opens upward.

Because of this symmetry, the vertex of the parabola occurs on the axis of symmetry, and thus the x-coordinate of the vertex is\[\frac{-b}{2a}\]

Answer 6

theres a much easier way to do that

Answer 7

what that method?

Answer 8

@kwinters, If you have an easier method than -b/2a, then why are you posting the question? Do it yourself, or ask your gadfly for help.