Question 172502
Let width = {{{w}}}
Let length = {{{l}}}
Let area = {{{A}}}
{{{3w + 2l = 1200}}}
{{{2l = 1200 - 3w}}}
{{{l = (1200 - 3w)/2}}}
{{{A = w*l}}}
{{{A = w*(1200 - 3w) / 2}}}
{{{A = 600w - (3/2)*w^2}}}
If I set {{{A=0}}} to find the roots, the 
maximum will be at {{{w[max] = -b/(2a)}}} which
is exactly 1/2 way between the roots
{{{-(3/2)*w^2 + 600w = 0}}}
{{{-b = -600}}}
{{{2a = -3}}}
{{{-b/(2a) = -600/-3}}}
{{{-600/-3 = 200}}}
{{{w = 200}}}
And, since
{{{3w + 2l = 1200}}}
{{{3*200 + 2l = 1200}}}
{{{2l = 600}}}
{{{l = 300}}}
The dimensions of the largest enclosure will
be when width = 200 ft and length = 300 ft
check answer:
{{{3w + 2l = 1200}}}
{{{3*200 + 2*300 = 1200}}}
{{{600 + 600 = 1200}}}
{{{1200 = 1200}}}
and
{{{A = w*l}}}
{{{A = 200*300}}}
{{{A = 60000}}} ft2
To see if this is max area change  {{{w}}} and {{{l}}}
slightly but still make {{{3w + 2l = 1200}}} true, like
{{{w = 200.1}}}
{{{l = 299.85}}}
{{{A = 299.85*200.1}}}
{{{A = 59999.985}}}
It ends up being a little less as it should