# 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?

Apr 8, 2018

$C \left(x\right) = 0.2 {x}^{2} - 12 x + 240$

$C ' \left(x\right) = 0.4 x - 12$

Equating this to 0,

$\implies 0.4 x - 12 = 0$

$\implies 0.4 x = 12$

$\implies x = 30$

Again, taking derivative of $C ' \left(x\right) = 0.4 x - 12$

$C ' ' \left(x\right) = 0.4$

$C ' ' \left(x\right) > 0$

Hence, $C \left(x\right) = 0.2 {x}^{2} - 12 x + 240$ is minimised at $x = 30$.

30 acres of flowers would minimize these costs :)