Question 906174
Let {{{ x }}} = number of apple trees added
Let {{{ y }}} = the yield for the orchard
----------------
{{{ y =  ( 40 + x )*( 500 - 10x ) }}}
{{{ y = 20000 + 500x - 400x - 10x^2 }}}
{{{ y = -10x^2 + 900x + 20000 }}}
-------------------------------
Find {{{ x[max] }}} and then {{{ y[max] }}}
-----------------
{{{ x[max] = -b/(2a) }}}
{{{ a = -10 }}}
{{{ b = 900 }}}
--------------
{{{ x[max] = -900/(2*(-10)) }}}
{{{ x[max] = 45 }}}
and
{{{ y[max] = -10*45^2 + 900*45 + 20000 }}}
{{{ y[max] = -20250 + 40500 + 20000 }}}
{{{ y[max] = 40250 }}}
-------------------
45 more trees will maximize yield
40,250 will be the maximum yield
-------------------------------------
Here's the plot:
{{{ graph( 500, 500, -30, 150, -4000, 45000, -10x^2 + 900x + 20000 ) }}} 
( note that {{{ x=0 }}} doesn't mean no apples- it means no ADDITIONAL apples )