Math 006 (Lecture 29)
Optimization
Strategy for solving optimization problems:
•
Step 1: Introduce variables, look for relationships among the variables, and construct
a mathematical model of the form
Maximize (or Minimize)
f
(
x
) on the interval
I
•
Step 2: Find the critical value(s) of
f
(
x
).
•
Step 3: Find the abolute maximum (or minimum) value of
f
(
x
) on the interval
I
and
the value(s) of
x
where this occurs.
•
Step 4: Use the solution to the mathematical model to answer all the questions asked
in the problem.
Example 1.
A homeowner has $320 to spend on building a fence around a rectangular
garden. Three sides of the fence will be constructed with wire fencing at a cost of $2 per
linear foot.
The fourth side is to be constructed with wood fencing at a cost of $6 per
linear foot. Find the dimensions and the area of the largest garden that can be enclosed
with $320 wroth of fencing.
1
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Example 2.
Refer to Example 1. The homeowner judges that an area of 800 square feet
for the garden is too small and decides to increase the area to $1,250 square feet. What
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 Fall '09
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 Math, Optimization, square feet, mathematical model

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