Question 417894
Let {{{x}}} = number of trees to be added
Let {{{Y}}} = yield from orchard
{{{Y = 400*(30 + x) - 10x*( 30 + x) }}}
{{{Y = (400 - 10x)*(30 + x) }}}
{{{ Y = 12000 - 300x + 400x - 10x^2 }}}
{{{Y = -10x^2 + 100x + 12000}}}
The maximum of a quadratic is at {{{ -b/(2a) }}}
{{{-b/(2a) = -100/(-20) }}}
{{{-100/(-20) = 5}}}
5 trees should be added to maximize yield
The yield, {{{Y}}}, is
{{{Y = -10*5^2 + 100*5 + 12000}}}
{{{Y = -250 + 500 + 12000}}}
{{{Y = 12250}}}
Here's a plot:
{{{ graph( 400, 400, -20, 60, -1000, 15000, -10x^2 + 100x + 12000) }}}