Question 1025104
Let the numbers be {{{ x }}} and {{{ y }}}
{{{ x = (1/3)*y + 10 }}}
The product is:
{{{ x*y }}}
{{{ (1/3)*y + 10 = x }}}
{{{ (1/3)*y = x - 10 }}}
{{{ y = 3x - 30 }}}
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{{{ x*y = x*( 3x - 30 ) }}}
{{{ x*y = 3x^2 - 30x }}}
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The formula for minimum is:
{{{ x[min] = -b/(2a) }}}
{{{ x[min] = -(-30) / ( 2*3 ) }}}
{{{ x[min] = 5 }}}
and
{{{ y = 3x - 30 }}}
{{{ y = -15 }}}
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When the numbers are 5 and -15, the product is a minimum
The minimum product is {{{ 5*(-15) = -75 }}}
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check:
Suppose {{{ x = 5.1 }}}
{{{ y = 3x - 30 }}}
{{{ y = 15.3 - 30 }}}
{{{ y = -14.7 }}}
{{{ x*y = 5.1*14.7 }}}
{{{ x*y = -74.97 }}}
This is larger than {{{ -75 }}}, so 
{{{ 5*(-15) }}} seems to be the minimum