Answer
$850$ vines.
Work Step by Step
We can rewrite our quadratic function in the usual form by redistributing the factors:
$A(n)=(700+n)(10-0.01n)$
$A(n)=700*10-700*0.01n+10n-0.01n^2$
$A(n)=7000-7n+10n-0.01n^2$
$A(n)=-0.01n^2+3n+7000$
In this function, $a=-0.01$, $b=3$, $c=7000$, where $n$ represents the number of additional vines.
Production - $A(n)$ - is maximized when the number of additional vines is:
$n=\frac{-b}{2a}=\frac{-3}{-0.02}=150$
Therefore, the number of vines per acre that should be planted is:
$700+150=850$ vines.
