Section 4.6 – Optimization
To optimize is to find the BEST way of doing something.
Example. We can maximize things like area, volume, profit, height…
We can minimize things like time, distance, cost…
Steps
1.
Understand the problem.
Read it carefully and identify the important
information.
2.
Draw a
picture if possible.
3.
Define the variables; identify what is to maximized or minimized.
4.
Find an equation that relates variables.
5.
Write a function of one variable .
6.
Use methods from sections 4.2 and 4.3 to find the absolute extreme values.
Class and Extra Problems
1.
A right triangle is formed in the first quadrant by the x and yaxes and a line
through the point (2, 3).
Find the vertices of the triangle so that its area is
minimized.
2.
The wall of a building is to be braced by a beam that must pass over a parallel
fence 5 feet high and 4 feet from the building.
Find the length of the shortest
beam that can be used.
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 Spring '08
 dempster/mccolum
 Math, International System of Units, Imperial units, adjacent rectangular corrals, rectangular dog pen

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