jmc

Let the length of the enclosure be $l$ and the width be $w$. We have the equation $2l+2w=300\Rightarrow l+w=150$. We want to maximize the area of this rectangular tennis court, which is given by $lw$. From our equation, we know that $l=150-w$. Substituting this into our expression for area, we have $$(150-w)(w)=150w-w^2$$We will now complete the square to find the maximum value of this expression. Factoring a $-1$ out, we have $$-(w^2-150w)$$In order for the expression inside the parentheses to be a perfect square, we need to add and subtract $(150/2{)}^2=5625$ inside the parentheses. Doing this, we get $$-(w^2-150w+5625-5625)\Rightarrow -(w-75{)}^2+5625$$The expression is maximized when $-(w-75{)}^2$ is maximized, or in other words when $(w-75{)}^2$ is minimized. Thus, we wish to make $w$ as close as possible to 75, considering the condition that $l\ge 80$. When $l=80$, $w=150-l=70$. Since as $l$ increases, $w$ decreases further below 70, the optimal dimensions are $l=80$ and $w=70$. Hence, the optimal area is $lw=80\cdot 70=\boxed{5600}$ square feet.