Question 1139816
At break-even point, {{{ P(x) = 0 }}}
{{{ -60x^2 + 1800x - 7500 = 0 }}}
{{{ -x^2 + 30x - 125 = 0 }}}
{{{ ( -x + 25 )*( x - 5 ) = 0 }}} ( by looking at it )
{{{ x = 25 }}}
{{{ x = 5 }}}
5 or 25 statues/mo give zero profit ( break even )
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The x-value of {{{ P[max] }}} is:
{{{ P[max] = -b/(2a) }}}
{{{ P[max] = -1800/(2*(-60)) }}}
{{{ P[max] = 1800/120 }}}
{{{ P[max] = 15 }}}
15 item/mo will maximize profit
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{{{ P(15) = -60*15^2 + 1800*15 - 7500 }}}
{{{ P[max] = -60*225 + 27000 - 7500 }}}
{{{ P[max] = -13500 + 27000 - 7500 }}}
{{{ P[max] = 6000 }}}
$6000 is max profit
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Here's the plot:
{{{ graph( 400, 400, -3, 30, -700, 7000, -60x^2 + 1800x - 7500 ) }}}