Chapter 4.4.notebook
October 28, 2014
Chapter 4.4 Optimization Problems
pg. 223
1. Read and organize your information as 'given' and 'find'
2. Write the objective function (the equation to find max and/or min)
3. Identify the constraint equation; This is usually some other relationship between the
variables.
4. Use the constraints to write the objective function as a function of a single variable.
5. Find the interval (domain) of interest.
6. Use calculus to find absolute max or min (check endpoints)
Example: Maximum-volume box.
Suppose an airline policy states that all baggage must be box shaped with a sum of
length, width, and height not exceeding 108 in. What are the dimensions and
volume of a square-based box with greatest volume under these conditions?
Sep 5-2:31 PM
1
Chapter 4.4.notebook
October 28, 2014
Chapter 4.4 Optimization Problems
Example: Maximum-volume box.
Suppose an airline policy states that all baggage must be box shaped with a sum of
length, width, and height not exceeding 108 in. What are the dimensions and
volume of a square-based box with greatest volume under these conditions?
Sep 5-2:31 PM
2
Chapter 4.4.notebook
October 28, 2014
Chapter 4.4 Optimization Problems
pg. 223
1. Read and organize your information as 'given' and 'find'
2. Write the objective function (the equation to find max and/or min)
3. Identify the constraint equation; This is usually some other relationship between the
variables.
4. Use the constraints to write the objective function as a function of a single variable.
5. Find the interval (domain) of interest.
6. Use calculus to find absolute max or min (check endpoints)
Example: Minimum distance.
Find the point P on the curve of y = x2 that is closest to the point (18,0). What is the
least distance between P and (18,0)?
Sep 5-2:31 PM
3
Chapter 4.4.notebook
October 28, 2014
Chapter 4.4 Optimization Problems
Example: Minimum distance.
Find the point P on the curve of y = x2 that is closest to the point (18,0). What is the
least distance between P and (18,0)?
Sep 5-2:31 PM
4
Chapter 4.4.notebook
October 28, 2014
Chapter 4.4 Optimization Problems
pg. 223
1. Read and organize your information as 'given' and 'find'
2. Write the objective function (the equation to find max and/or min)
3. Identify the constraint equation; This is usually some other relationship between the
variables.
4. Use the constraints to write the objective function as a function of a single variable.
5. Find the interval (domain) of interest.
6. Use calculus to find absolute max or min (check endpoints)
Example: Minimum time
Standing on the shore of a circular pond with radius 1 mile and you want to get to a
point on the shore completely opposite your position. You plan to swim at 2mi/hr
from your current position to another point P on the shore and then walk at 3 mi/hr to
the final destination. How should you choose P to minimize the total time for the
trip?
finish F
start S
Sep 5-2:31 PM
5
Chapter 4.4.notebook
October 28, 2014
Chapter 4.4 Optimization Problems
Example: Minimum time
Standing on the shore of a circular pond with radius 1 mile and you want to get to a
point on the shore completely opposite your position. You plan to swim at 2mi/hr
from your current position to another point P on the shore and then walk at 3 mi/hr to
the final destination. How should you choose P to minimize the total time for the
trip?
finish F
start S
Sep 5-2:31 PM
6
Chapter 4.4.notebook
October 28, 2014
Chapter 4.4 Optimization Problems
Example: Minimum time
Standing on the shore of a circular pond with radius 1 mile and you want to get to a
point on the shore completely opposite your position. You plan to swim at 2mi/hr
from your current position to another point P on the shore and then walk at 3 mi/hr to
the final destination. How should you choose P to minimize the total time for the
trip?
finish F
start S
Sep 5-2:31 PM
7
Chapter 4.4.notebook
October 28, 2014
Oct 25-1:40 PM
8