Question 1111261
Profit is {{{R-C}}}


{{{-x^2+220x-60x-3000}}}

{{{-x^2+160x-3000}}}


Maximum will be at exact middle of the two roots.


roots  {{{(-160+- sqrt(160^2-4(-1)(-3000)))/(-2)}}}


{{{(-160+- sqrt(160^2-12000))/(-2)}}}


{{{(-160+- sqrt(13600))/(-2)}}}


{{{(-160+- sqrt(4*34*10*10))/(-2)}}}


{{{(-160+- 20*sqrt(34)/(-2)}}}


{{{80+- 10*sqrt(34)}}}


Exact middle of these is at {{{highlight_green(x=80)}}}.

{{{-x^2+160x-3000}}}
{{{-6400+160*80-3000}}}
{{{highlight(3400)}}}---------maximum profit