Question 255888
We have two formulas:
(i) {{{P = 2x + y}}}, where p =1000. Note we only have 3 sides.
(ii) {{{A = xy}}}
From (i) we get
(iii) {{{1000 = 2x + y}}}
Solve (iii) for y to get
(iv) {{{y = 1000-2x}}}
substitute (iv) into (ii) to get
(v) {{{A = x(1000-2x)}}}
which is
(vi) {{{A = -2x^2 + 1000x}}}
set -2x^2 + 1000x = 0  and create vertex form as
{{{(x-250)^2 + 125000}}}
so the max area is 125,000 sq. ft.