SOLUTION: A farmer uses 1200 feet of fence to enclose a rectangular region and also to subdivide the region into three smaller rectangular regions by placing fences parallel to one of the si
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Question 163093This question is from textbook
: A farmer uses 1200 feet of fence to enclose a rectangular region and also to subdivide the region into three smaller rectangular regions by placing fences parallel to one of the sides. Find the dimensions that produce the greatest enclosed area. This question is from textbook
You can put this solution on YOUR website! A farmer uses 1200 feet of fence to enclose a rectangular region and also to
subdivide the region into three smaller rectangular regions by placing fences
parallel to one of the sides. Find the dimensions that produce the greatest
enclosed area.
:
If you draw this out, you can see that total fence equation will be:
2L + 4W = 1200
Simplify, divide by 2
L + 2W = 600
L = (600-2W)
:
Area;
A = L*W
Substitute (600-2W) for L:
A = (600-2W)*W
A = -2W^2 + 600W; a quadratic equation
:
The dimension that will produce the greatest area will be the "axis of symmetry
which is: x =
:
In this equation a=-2, b=600
W =
W =
W = +150 ft is the width
:
Find the length
L = 600 - 2(150)
L = 300 ft is the length
:
We can say the a field 300 by 150 gives he greatest area
:
This illustrated on a graph where y axis is the area and x axis is the width:
