Question 1014285
Let {{{ n }}} = number of $1 increases in price
Let {{{ R }}} = daily revenue
{{{ R = ( 30 + 3n )*( 19 - 1*n ) }}}
{{{ R = 570 + 57n - 30n - 3n^2 }}}
{{{ R = -3n^2 + 27n + 570 }}}
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Note that if there are no reductions in price ( {{{ n=0 }}} )
Then {{{ R = 570 }}} which is {{{ R = 30*19 }}}
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What is the other value of {{{ n }}} that gives me {{{ R = 570 }}} ?
{{{ R = -3n^2 + 27n + 570 }}}
{{{570 = -3n^2 + 27n + 570 }}} 
{{{ -3n^2 + 27n = 0 }}}
{{{ n*( -3n + 27 ) = 0 }}}
{{{ -3n + 27 = 0 }}}
{{{ 3n = 27 }}}
{{{ n = 9 }}}
Her revenue will be equal to or greater than $570 if the
$1 increases are between {{{ 0 }}} and {{{ 9 }}}
That converts to price ranges of:
{{{ 19 - 1*0 = 19 }}} dollars/shirt
to
{{{ 19 - 1*9 = 10 }}} dollars/shirt
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Here's a plot of  {{{ R }}} and {{{n }}}
and {{{ R = 570 }}}
{{{ graph( 400, 400, -2, 12, -50, 700, -3x^2 + 27x + 570, 570 ) }}}