Solutions to Quiz 8A
www.math.ufl.edu/˜harringt
November 26, 2006
1.
(3 pts.)
Mrs. Zerta wants to start a garden next to her house. She only has 400
yards of fencing. If fencing is NOT required along side of her house, what are the
dimensions of the largest area that she can enclose? What is this area?
Solution:
We will let
x
denote the width and
y
denote the length.
So we
have this image:
So we have that the perimeter is
P
= 2
x
+
y
= 400.
Also recall that the area
is:
A
=
xy
.
Thus, we will solve for
y
using the perimter.
So,
y
= 400

2
x
.
Next, we will substitute
y
= 400

2
x
back in the formula for area.
Hence,
A
=
x
(400

2
x
) = 400
x

2
x
2
. This is the equation we want to maximize. Also
note that,
x
≥
0, and
y
= 400

2
x
≥
0. So, 0
≤
x
≤
200. Therefore, we want
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 Spring '08
 Smith
 Math, Calculus, 1 pt, Logarithm, 1 pts

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