# 1. Shipping regulations A shipping company requires that the sum of length plus girth of rectangular

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1. Shipping regulations A shipping
company requires that the sum of length plus girth of rectangular boxes not
exceed 108 in. Find the dimensions of the box with maximum volume that meets this
condition. (The girth is the perimeter of the smallest side of the box.)

2. Box with minimum surface area Find
the dimensions of the rectangular box with a volume of 16 ft3 that
has minimum surface area.

3. Extreme distances to an ellipse Find
the minimum and maximum distances between the ellipse x2 +
xy
+
2y2 =
1
and the origin.

4. Maximum area rectangle in an ellipse Find
the dimensions
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1. Shipping regulations A shipping
company requires that the sum of length plus girth of rectangular boxes not
exceed 108 in. Find the dimensions of the box with maximum volume that meets this
condition. (The girth is the perimeter of the smallest side of the box.)

2. Box with minimum surface area Find
the dimensions of the rectangular box with a volume of 16 ft3 that
has minimum surface area.

3. Extreme distances to an ellipse Find
the minimum and maximum distances between the ellipse x2 +
xy
+
2y2 =
1
and the origin.

4. Maximum area rectangle in an ellipse Find
the dimensions of the rectangle of maximum area with sides parallel to the
coordinate axes that can be inscribed in the ellipse 4×2 +
16y2 =
16.

5. Maximum perimeter rectangle in an
ellipse Find
the dimensions of the rectangle of maximum perimeter with sides parallel to the
coordinate axes that can be inscribed in the ellipse 2×2 +
4y2 =
3.

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