A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals....

diferira7c

diferira7c

Answered

2021-12-25

A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals. What dimensions should be used so that the enclosed area will be a maximum?

Answer & Explanation

amarantha41

amarantha41

Expert

2021-12-26Added 38 answers

To get the dimensions of our rectangle, we must first determine x and y.
We can see from the sketch that we have
2x+3y=400x=20032y
Our area is
A(x,y)=2xy
As we can see from the first equation, our function is
A(x,y)=2xy
We can see from the first equation that we have So our function is
A(x,y)=2xy
A(y)=2(20032y)y
A(y)=(4003y)y
A(y)=3y2+400y
The first step is to identify critical numbers and solve them -
A(y)=0
This leads to 
A(y)=6y+400
So our equation becomes
6y+400=0y=2003
When we plug this into expression for x, we get
x=20032yx=100
As a result, our ultimate dimensions are
x=100;y=2003

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