Homework 10
Directions: Similar problems may appear on the final. This assignment is not turned in for credit.

Suppose someone owns 4000 meters of fencing. They wish to create a rectangular piece
of grazing land where one side is along a river. This means no fence is needed for that
side. Moreover, they wish to subdivide the rectangle into three separate sections with two pieces
of fence, both of which are parallel to the sides not along the river. What are the dimensions of the largest area that can be enclosed?
 By cutting away identical squares from each
corner of a rectangular piece of cardboard and folding up
the resulting flaps, an open box may be made. If the cardboard
is 15 in. long and 8 in. wide, find the dimensions of
the box that will yield the maximum volume.
 Find the dimensions of a rectangle with a perimeter of
100 ft that has the largest possible area.
 Find the absolute extrema, if any, of \[f(x) = \dfrac{1}{2}x^2  2\sqrt{x}\qquad [0, 3]\]