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Lesson 14  Optimization
1
Lesson 14
Optimization
Now you’ll work some problems where the objective is to optimize a function.
That
means you want to make it as large as possible or as small as possible depending on the
problem.
In many problems, you’ll state the domain before you work the problem.
Once you have
the function and its domain, you’ll find the critical points and see if the critical point(s)
fall within the domain of the function.
You can also use the second derivative test to
verify that you have an absolute max or an absolute min in many problems.
Example 1:
A company that produces digital cameras wants to minimize its production
costs.
They estimate that their total monthly cost for producing the camera is given by
10000
x
80
2
x
0025
.
0
)
x
(
C
+
+
=
.
Find the average cost function.
Find the level of
production that results in the smallest average production cost.
Use the second derivative
test to verify that you have found a minimum cost.
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This note was uploaded on 02/15/2011 for the course MATH 1313 taught by Professor Constante during the Fall '08 term at University of Houston.
 Fall '08
 CONSTANTE

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