1. Applications of Extrema
Lesson 6.2

2. A Rancher Problem You have 500 feet of fencing for a corral
What is the best configuration (dimensions) for a rectangular corral to get the most area
One side of the rectangle already has a fence

3. Sample Problem
Your assistant presents you with a contract for signature
Your firm offers to deliver 300 tables to a dealer at $90 per table and to reduce the price per table on the entire order by $0.25 for each additional table over 300
What should you do?
Find the dollar total involved in largest (smallest) possible transaction between the manufacturer and the dealer.

4. Solution Strategy Read the problem carefully From our problem
Make sure you understand what is given
Make sure you see what the unknowns are
From our problem
Given
300 tables at $90 per table
$0.25 reduction per table on entire order if > 300
Unknowns
Largest possible transaction
Smallest possible transaction

5. Solution Strategy If possible sketch a diagram From our problem
Label the parts
From our problem
Not much to diagram …
More likely in a problem about the size of a box to minimize/maximize materials or volume
x + 3 x 2x

6. Solution Strategy Decide on a variable to be maximized (minimized)
Express variable as a function of one other variable
Be sure to find function domain
From our problem
T = transaction amount
T = f(x) = ?

7. Solution Strategy
To analyze the function, place it in Y= screen of calculator
Check the table (♦Y) to evaluate the domain and range for setting the graph window

8. Solution Strategy Find the critical points for the function
View on calculator
For our problem
Use derivative tests to find actual points

9. Solution Strategy If domain is closed interval For our problem
Evaluate at endpoints, critical points
See which value yields absolute max or min
For our problem

10. Strategy Review Read carefully, find knowns, unknowns
Sketch and label diagram
Determine variable to be max/min
Express as function of other variable
Determine domain
Find critical points
If domain is closed interval
Check endpoints
Check critical points

11. Practice Problem
A fence must be built to enclose a rectangular area of 20,000 ft2
Fencing material costs $3/ft for the two sides facing north and south
It costs $6/ft for the other two sides
Find the cost of the least expensive fence

12. Assignment
Lesson 6.2
Page 383
Exercises 5 – 33 odd