Asked by Bri
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.)
Answers
Answered by
bobpursley
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
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
Answered by
Steve
And, note that this maximum area occurs when the fencing is equally split among lengths and widths.
Answered by
abity
shiuldn't it be p=4w+3L
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