# Math Help - Optimization Problem !

1. ## Optimization Problem !

Suppose the revenue (in thousands) for sales of x hundred units of an electronic item is given by the function R(x) = 40x^2e^-0.4x + 30, where the max capacity of the plant is eight hundred. Determine number of units for max revenue.

Suppose the revenue (in thousands) for sales of x hundred units of an electronic item is given by the function R(x) = 40x^2e^-0.4x + 30, where the max capacity of the plant is eight hundred. Determine number of units for max revenue.
$R^{\prime}(x) = 80xe^{-0.4x} - 16x^2e^{-0.4x} = 0$ <-- Solve for x

$80xe^{-0.4x} = 16x^2e^{-0.4x}$

$5 = x$

(I leave it to you to prove that x = 5 is a local maximum, not a local minimum.)

-Dan

Edit: This problem would actually belong to a Calculus forum...

3. So you are saying the maximum number of units is 5, but the answer is 500 at back of book? Or am I totally confused. Thanks.