Question 1130474
{{{ P(N) = 0 }}} ( zero profit )
{{{ -.2N^2 + 3.6N - 9 = 0 }}}
{{{ N = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = -.2 }}}
{{{ b = 3.6 }}}
{{{ c = -9 }}}
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{{{ N = (-3.6 +- sqrt( 3.6^2-4*(-.2)*(-9) ))/(2*(-.2)) }}}
{{{ N = (-3.6 +- sqrt( 12.96 - 7.2 ))/((-.4)) }}}
{{{ N = (-3.6 +- sqrt( 5.76 ))/((-.4)) }}}
{{{ N = ( -3.6 + 2.4 )/ (-.4 ) }}}
{{{ N = (-1.2)/(-.4) }}}
{{{ N = 3 }}}
and
{{{ N = ( -3.6 - 2.4 ) / (-.4) }}}
{{{ N = 6/.4 }}}
{{{ N = 15 }}}
The two break even points are
{{{ N = 3 }}} and {{{ N = 15 }}}
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check:
{{{ -.2N^2 + 3.6N - 9 = 0 }}}
{{{ -.2*15^2 + 3.6*15 - 9 = 0 }}}
{{{ -.2*225 + 54 - 9 = 0 }}}
{{{ -45 + 54 - 9 = 0 }}}
{{{ 0 = 0 }}}
OK
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