Applications of Extrema Lesson 6 2 A Rancher

A Rancher Problem You have 500 feet of fencing for a corral What is

Sample Problem Your assistant presents you with a contract for signature • Your firm

Solution Strategy Read the problem carefully 1. • • Make sure you understand what

Solution Strategy If possible sketch a diagram 2. • Label the parts From our

Solution Strategy Decide on a variable to be maximized (minimized) • Express variable as

Solution Strategy To analyze the function, place it in Y= screen of calculator Check

Solution Strategy Find the critical points for the function 4. • View on calculator

Solution Strategy If domain is closed interval 5. • • Evaluate at endpoints, critical

Strategy Review Read carefully, find knowns, unknowns Sketch and label diagram Determine variable to

Practice Problem A fence must be built to enclose a rectangular area of 20,

Assignment Lesson 6. 2 Page 383 Exercises 5 – 33 odd 12

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Applications of Extrema Lesson 6. 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 2

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. 3

Solution Strategy Read the problem carefully 1. • • 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 4

Solution Strategy If possible sketch a diagram 2. • 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 2 x x 5

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) = ? 6

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 7

Solution Strategy Find the critical points for the function 4. • View on calculator For our problem • Use derivative tests to find actual points 8

Solution Strategy If domain is closed interval 5. • • Evaluate at endpoints, critical points See which value yields absolute max or min For our problem 9

Strategy Review Read carefully, find knowns, unknowns Sketch and label diagram Determine variable to be max/min 1. 2. 3. • • Express as function of other variable Determine domain Find critical points If domain is closed interval 4. 5. • • Check endpoints Check critical points 10

Practice Problem A fence must be built to enclose a rectangular area of 20, 000 ft 2 • 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 11

Assignment Lesson 6. 2 Page 383 Exercises 5 – 33 odd 12