Question 697046
Let {{{ C }}} = the cost to produce {{{ n }}} DVD's
which do not include the {{{ 200 }}} samples
The $300,000 is a fixed cost, and the {{{ 200 }}}
that are given away is a fixed cost. This fixed cost 
is the {{{ 200*.27 }}} production cost of 
the samples
{{{ C = .27n + 300000 + 200*.27  }}}
{{{ C = .27n + 300000 + 54 }}}
{{{ C = .27n + 300054 }}}
The average cost is required to be
{{{ C / ( n + 200 ) < 12 }}}
Substituting,
{{{ ( .27n + 300054 ) / ( n + 200 ) < 12 }}}
{{{ .27n + 300054  < 12*( n + 200 ) }}}
{{{ .27n + 300054 < 12n + 2400 }}}
{{{ 11.73n > 300054 - 2400 }}}
{{{ 11.73n > 297654 }}}
{{{ n > 25375.5 }}}
{{{ n + 200 > 25575.5 }}}
25,577 DVDs must be produced for the 
average cost to be under $12
-----------------
check answer:
{{{ C = .27n + 300054 }}}
{{{ C = .27*25377 + 300054 }}}
{{{ C = 6851.79 + 300054 }}}
{{{ C = 306905.79 }}}
{{{ C / ( n + 200 ) < 12 }}}
{{{ 306905.79 / ( n + 200 ) < 12 }}} 
{{{ 306905.79 / ( 25377 + 200 ) < 12 }}} 
{{{ 306905.79 / 25577 < 12 }}}
{{{ 11.999 < 12 }}}
OK
Hope I got it!