SOLUTION: A farmer needs to build a fence with 2 equal size pens to separate the sheep and pigs. The farmer will build a rectangular outer fence plus a dividing fence down the middle paralle
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Question 760995: A farmer needs to build a fence with 2 equal size pens to separate the sheep and pigs. The farmer will build a rectangular outer fence plus a dividing fence down the middle parallel to two sides. If she has a total of 200 feet of fencing, find the dimensions that will enclose the maximum total area.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
x for length of the whole area, and y for the width of the whole area. Choose y longer than x, and so take the divider parallel to x.
Accounting for fencing material, .
Accounting for area,
Perimeter equation gives
Substitute into area equation.
A looks like a quadratic equation as a function, and indicates a parabola with a maximum ( openings downward). Finding the zeros is very easy, only requiring back one step in deriving A(x). The maximum A for AREA will occur directly in the middle of the two zeros of A(x).
ZEROS of A:
Either x=0
OR
100-(3/2)x=0
Maximum Area occurs at
To find y,
----------------------------------More about the area-----------
This area maximum is:
A(100/3)=100(100/3)-(3/2)(100/3)^2
A=10000/3-(3/2)*10000/9
A=1000/3-3*10000/18
A=6*10000/18-3*10000/18
A=3*10000/(3*6)=10000/6
A=1667 square feet
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