Worksheet ----MS125 Calculus I Dr. Y. Kim
4.6 Applied Optimization
Ex1) Find positive numbers
x
,
y
such that 16
=
xy and
y
x
+
is as small as possible.
Ex2) A piece of wire of length L is bent into the shape of a rectangle. Which dimensions produce the
rectangle of maximum area?
Ex3) What are the dimensions of an aluminum can that holds 40 in
3
of juice and that uses the least material?
Assume that the can is cylindrical, and is capped on both ends.
HOMEWORK ----------------4,11,13,16,18,24
Practical Tips for Modeling Optimization Problems
1. Make sure that you know what quantity or function to be optimized.
2. If possible, make several sketches showing how the elements that vary are related.
Label your sketches clearly by assigning variables to quantities which change.
3. Try to obtain a formula for the function to be optimized in terms of the variables
that you identified in the previous step. If necessary, eliminate from this formula
all but one variable. Identify the domain over which this variable varies.
4. Find the critical points and evaluate the function at these points and the endpoints
to find the absolute maximum and minimum.