HELP!!! Find the number of units that produces a maximum revenue. The revenue R is measured in dollars and x

is the number of units produced.

R = 80x – 0.0002x^2

I have no idea where to begin with this problem so could anyone help me by writing out the steps? Thank you!!

Candice -

This is a parabola. Also, the parabola opens downward because the coefficient in front of x^2 is negative. So, the maximum will happen at the "vertex" of the parabola.

You might remember that the vertex of a parabola equals (-b/2a). In your problem

a = -0.0002
b = 80

So the x-coordinate of the vertex = - (80/ [(2)(-0.0002)] = 200,000

So the number of units is 200,000

The revenue R = 80x – 0.0002x^2 = 80(200,000) -(0.0002)(200,000)^2

R = $8 million

Hope that helped

The previous poster is right. However, a simpler way to figure it out is to get the derivative and set that equal to zero. You might not know calculus, but this is a very simple derivative.*

R = 80x - 0.0002x^2

dR/dx = 80 - 2*0.0002x

0 = 80 - 0.0004x
0.0004x = 80
x = 200,000 units


*if you don't know how to do simple derivatives, the rule is if y = ax^n +bx + c (where a, b, and c are constants), the derivative, dy/dx = n*ax^(n-1) + b

multiply both sides by .0002

.0002R=.016x-x^2
x^2-.016x-.0002R=0