A rectangle field is to be enclosed by fencing. In addition to the enclosing fence,another fence is divide the field into two parts,running parallel to two sides.IF 1,200 feet of fencing is available, find the maximum area that can be enclosed?

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Answer 1 · 2018-06-15T23:42:32

I don't see how the dividing fence helps, if it's not one of the sides. Let's ignore it.

Maximize #S=xy# subject to #2x + 2y = 1200#

#y=600-x#

#S = x(600-x) = -x^2+600x = -(x^2 - 600 x + 300^2) + 300^2 = -(x-300)^2+300^2#

Clearly a maximum area of #S=300^2=90000# square feet when #x=y=300# feet.