Find the dimensions of the rectangular corral split into 2 pens of the same size producing the greatest possible enclosed area given 300 feet of fencing. (Assume that the length is greater than or equal to the width.)

Answer 1

Perimeter=3W+3L (makes two pens)

Area=WL

300=3W+2L
L=150-1.5W

Area=W(150-1.5W)
= 150W-1.5W^2

this is a parabola, in standard form
w^2-100w+Area/1.5=0
a=1 b=-100 c=area/1.5

maximum=-b/2a=100/2=50

http://www.wikihow.com/Find-the-Maximum-or-Minimum-Value-of-a-Quadratic-Function-Easily

Answer 2

And, note that this maximum area occurs when the fencing is equally split among lengths and widths.

Answer 3

shiuldn't it be p=4w+3L