The weekly cost (C) of growing and selling x acres of flowers is approximated by C = 0.2x^2-12x + 240. How many acres of flowers would minimize these costs?

Sep 28, 2015

I found $30$ acres.

Explanation:

You can take the derivative in $x$ (acres) of your function and set it equal to zero. This will give you the $x$ value when your function (in this case) has a minimum (=zero slope):
Your function:$C \left(x\right) = 0.2 {x}^{2} - 12 x + 240$
Derive:
$C ' \left(x\right) = 0.2 \cdot 2 x - 12 = 0.4 x - 12$
set it equal to zero:
$C ' \left(x\right) = 0$ or:
$0.4 x - 12 = 0$
$x = \frac{12}{0.4} = 30$ acres.