Question 1182146


given:

{{{C = 50x + 400}}}

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

find profit:

{{{P=R-C}}}

{{{P=100x -0.5x^2-(50x + 400)}}}

{{{P=100x -0.5x^2-50x - 400}}}

{{{P= -0.5x^2+50x - 400}}}

if {{{P=400}}}

{{{400= -0.5x^2+50x - 400}}}

{{{0= -0.5x^2+50x - 400-400}}}

{{{0= -0.5x^2+50x - 800}}}....factor

{{{0= -0.5(x^2-100x +1600)}}}

{{{0= -0.5(x^2-20x -80x+1600)}}}

{{{0= -0.5((x^2-20x) -(80x-1600))}}}

{{{0= -0.5(x(x-20) -80(x-20))}}}

{{{0 = -0.5 (x - 80) (x - 20)}}}

solutions:

{{{x=80}}}
{{{x=20}}}