Optimization Practice Problems
1. A rectangular field is to be fenced off along the bank of a river. If 200 yards of fencing are
available, what are the dimensions of a field that produce the maximum area?
2. An oil can is to be made in the form of a right circular cylinder to have a volume of 16
in3. Find the dimensions of the can that requires the least amount of material.
3. Find the dimensions of the rectangle of largest area which can be inscribed in the closed
region bounded by the x-axis, y-axis, and graph of y=8-x3 .
4. Find the point(s) on the curve y  25 
1 2
x that are closest to the origin.
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