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?

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Answer 1 · 2018-04-08T15:01:46

#C(x) = 0.2x^2-12x + 240#

#C'(x) = 0.4x-12#

Equating this to 0,

#=>0.4x-12=0#

#=>0.4x=12#

#=>x=30#

Again, taking derivative of #C'(x) = 0.4x-12#

#C''(x) = 0.4#

#C''(x) >0#

Hence, #C(x) = 0.2x^2-12x + 240# is minimised at #x=30#.

30 acres of flowers would minimize these costs :)