3.x articles are produced at a total cost of (2x^2+30x+20)naira and each is sold for (x/3+100) naira. Find the of x which gives the greatest profit?

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Answer 1 · 2018-08-12T10:26:18

3.x articles are produced at a total cost of #(2x^2+30x+20)# naira
and each is sold for #(x/3+100)# naira.

So sale price #=3x(x/3+100)=3x^2+300x#

Hence profit #P=2x^2+30x+20-3x^2-300x#

#=>P=20-x^2-270x#

#=>P=20-(x^2-2*x*135+135^2-135^2#

#=>P=20+18225-(x-135)^2#

So prfit will be maximua\m when #x=135#