Question 1043672
Let {{{ n }}} = the number of trees added to 1 acre
Let {{{ Y(n) }}} = the yield in bushels/acre
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[ yield in bushels/acre ] = [ bushels/tree ] x [ trees/acre ]
{{{ Y(n) = ( 40 - n )*( 20 + n ) }}}
{{{ Y(n) = 800 - 20n + 40n - n^2 }}}
{{{ Y(n) = -n^2 + 20n + 800 }}}
The n-value of the vertex ( which is a peak ) 
is given by the formula:
{{{ n[max] = -b/(2a) }}} when the equation has the form:
{{{ Y(n) = a*n^2 + b*n + c }}}
{{{ n[max] = (-20)/(2*-1) }}}
{{{ n[max] = 10 }}}
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The grower started with {{{ 20 }}} tree/acre and adds {{{ 10 }}}
more for max yield, so she should plant:
30 trees/acre
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check answer:
{{{ Y(10) = ( 40 - 10 )*( 20 + 10 ) }}}
{{{ Y(10) = 30*30 }}}
{{{ Y(10) = 900 }}}
Maximum yield is 900 bushels/acre
Here's the plot:
{{{ graph( 600, 600, -5, 50, -200, 1200, -x^2 + 20x + 800 ) }}}