Question 1207491
{{{C = 40x + 800}}}

and the revenue is given by

{{{R = 100x -0.5x^2}}}

Recall that profit is revenue minus cost.

{{{P=R-C}}}

{{{P=100x -0.5x^2-(40x + 800)}}}

{{{P=100x-0.5x^2-40x - 800}}}

{{{P= - 0.5x^2+60x - 800}}}


 two values of {{{x }}}(production level) that will create a profit of ${{{800}}}:


{{{800= -0.5x^2+60x - 800}}}

{{{800+0.5x^2-60x + 800=0}}}

{{{0.5x^2-60x + 1600=0}}}

{{{0.5(x^2-120x+3200)=0}}}

{{{0.5(x^2-40x-80x+3200)=0}}}

{{{0.5 (x - 80) (x - 40) = 0}}}


solutions:

{{{x=40}}}

{{{x=80}}}