Question 904079
{{{ A(n) = ( 600 + n )*( 10 - .01n ) }}}
{{{ A(n) = 6000 + 10n - 6n - .01n^2 }}}
{{{ A(n) = -.01n^2 + 4n + 6000 }}}
--------------------------------
This equation is in the form:
{{{ a*x^2 + b*x + c }}}
The vertex ( peak ) isd at:
{{{ -b/(2a) = -4/(2*(-.01)) }}}
{{{ -b/(2a) = 4/.02 }}}
{{{ -b/(2a) = 200 }}}
200 vines will maximize production
check:
{{{ A(199) = ( 600 + 199 )*( 10 - 1.99 ) }}}
{{{ A(199) = 799*8.01 }}}
{{{ A(199) = 6399.99 }}}
---------------------
{{{ A(201) = ( 600 + 201 )*( 10 - 2.01 ) }}}
{{{ A(201) = 801*7.99 ) }}}
{{{ A(201) = 6399.99 }}}
---------------------
{{{ A(200) =  ( 600 + 200 )*( 10 - 2 ) }}}
{{{ A(200) = 800*8 }}}
{{{ A(200) = 6400 }}}
OK