1. Optimization Problems
Section 3.7
Optimization Problems

2. Ex: Farmer John has 240 feet of fencing and wants to enclose a rectangular field that borders a straight river. If he needs no fence along the river, find the largest area the field can be.

3. Strategy for optimization
Draw a picture (if appropriate)
Write down all given information and equations
Find the function to be optimized
Use substitution so the function has 1 variable
Take the derivative
Set the derivative equal to zero

4. Ex: A manufacturer is making a box with an open lid
Ex: A manufacturer is making a box with an open lid. The box will have a square base and a surface area of 108 square inches. What dimensions will produce a box with the maximum volume?

5. Ex: A can of soup has a volume of 1000 cubic centimeters
Ex: A can of soup has a volume of 1000 cubic centimeters. Find the dimensions of the can that will minimize the materials used.

6. Homework
p. 223 # 3-7, 13, 17, 21, 22, 29