Question 707446
The profit is Revenue minus Cost, or {{{ P = R - C }}}
{{{ R = 100x - .5x^2 }}}
{{{ C = 60x + 300 }}}
{{{ R - C = 100x - .5x^2 - 60x - 300 }}}
{{{ P = 100x - .5x^2 - 60x - 300 }}}
Given:
{{{ P = 300 }}}
{{{ 300 = 100x - .5x^2 - 60x - 300 }}}
{{{ -.5x^2 + 100x - 60x - 600 = 0 }}}
{{{ -.5x^2 + 40x - 600 = 0 }}}
{{{ -x^2 + 80x - 1200 = 0 }}}
use quadratic formula
{{{x = (-80 +- sqrt( 80^2- 4*(-1)*(-1200) ))/(2*(-1)) }}}
{{{x = (-80 +- sqrt( 6400 - 4800 ))/(-2) }}}
{{{x = (-80 +- sqrt( 1600 ))/(-2) }}}
{{{ x = ( -80 + 40 ) / (-2) }}}
{{{ x = -40/ (-2) }}}
{{{ x = 20 }}}
and
{{{ x = ( -80 - 40 ) / (-2) }}}
{{{ x = 60 }}}
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According to answers they make a profit of $300/wk
if they sell 20 items or 60 items
check answers:
{{{ P = 100x - .5x^2 - 60x - 300 }}}
{{{ 300 = 100x - .5x^2 - 60x - 300 }}}
{{{ 300 = 100*20 - .5*20^2 - 60*20 - 300 }}}
{{{ 300 = 2000 - 200 - 1200 - 300 }}}
{{{ 300 = 2000 - 1700 }}}
{{{ 300 = 300 }}}
OK
and
{{{ 300 = 100*60 - .5*60^2 - 60*60 - 300 }}}
{{{ 300 = 6000 - 1800 - 3600 - 300 }}}
{{{ 300 = 6000 - 5700 }}}
{{{ 300 = 300 }}}
OK