Section 4.7. Optimization – the process of finding an optimal value- either a maximum or a minimum under strict conditions Problem Solving Strategy –

Slides:

Advertisements

Similar presentations

Calculus Applications Math Studies 1. a)Find the local extrema and identify them as either a local maximum or a local minimum. b)Find the coordinates.

Advertisements

3.7 Modeling and Optimization

Guidelines for Solving Applied Minimum and Maximum Problems 1.Identify all given quantities and quantities to be determined. If possible, make a sketch.

Section 5.4 I can use calculus to solve optimization problems.

OPTIMIZATION PROBLEMS Section 3.7. When you are done with your homework, you should be able to… Solve applied minimum and maximum problems.

3.7 Optimization Problems

MAX - Min: Optimization AP Calculus. OPEN INTERVALS: Find the 1 st Derivative and the Critical Numbers First Derivative Test for Max / Min –TEST POINTS.

Optimization 4.7. A Classic Problem You have 40 feet of fence to enclose a rectangular garden along the side of a barn. What is the maximum area that.

4.4 Optimization Finding Optimum Values. A Classic Problem You have 40 feet of fence to enclose a rectangular garden. What is the maximum area that you.

Reminder: The Extreme Value Theorem states that every continuous function on a closed interval has both a maximum and a minimum value on that interval.

4.5 Optimization Problems Steps in solving Optimization Problems 1.Understand the Problem Ask yourself: What is unknown? What are the given quantities?

4.4 Modeling and Optimization What you’ll learn about Examples from Mathematics Examples from Business and Industry Examples from Economics Modeling.

Using Calculus to Solve Optimization Problems

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.

CHAPTER 3 SECTION 3.7 OPTIMIZATION PROBLEMS. Applying Our Concepts We know about max and min … Now how can we use those principles?

Applied Max and Min Problems

Section 14.2 Application of Extrema

Section 4.4: Modeling and Optimization

Do Now: ….. greatest profit ….. least cost ….. largest ….. smallest

Section 4.4 Optimization and Modeling

4.7 Optimization Problems

Lesson 4-7 Optimization Problems. Ice Breaker Using a blank piece of paper: Find the extrema (maximum) of A(w) = 2400w – 2w² A’(w) = 2400 – 4w A’(w) =

4.4 Modeling and Optimization Buffalo Bill’s Ranch, North Platte, Nebraska Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly,

Optimization. Objective  To solve applications of optimization problems  TS: Making decisions after reflection and review.

4.7 Optimization Buffalo Bill’s Ranch, North Platte, Nebraska Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1999.

Miss Battaglia AB/BC Calculus. We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field.

Optimization Section 4.7 Optimization the process of finding an optimal value – either a maximum or a minimum under strict conditions.

Warmup- no calculator 1) 2). 4.4: Modeling and Optimization.

Section 4.5 Optimization and Modeling. Steps in Solving Optimization Problems 1.Understand the problem: The first step is to read the problem carefully.

Optimization Problems

Optimization Problems

Sir Isaac Newton 1643 – 1727 Sir Isaac Newton 1643 – 1727 Isaac Newton was the greatest English mathematician of his generation. He laid the foundation.

Optimization. First Derivative Test Method for finding maximum and minimum points on a function has many practical applications called Optimization -

2/14/2016 Perkins AP Calculus AB Day 12 Section 3.7.

Optimization Problems Section 4-4. Example  What is the maximum area of a rectangle with a fixed perimeter of 880 cm? In this instance we want to optimize.

A25 & 26-Optimization (max & min problems). Guidelines for Solving Applied Minimum and Maximum Problems 1.Identify all given quantities and quantities.

Calculus Section 4.5 Solve max/min problems Recall: The max/min value of a function occurs at a point where the derivative of the function is either zero.

4.4 Modeling and Optimization, p. 219 AP Calculus AB/BC.

Sec 4.6: Applied Optimization EXAMPLE 1 An open-top box is to be made by cutting small congruent squares from the corners of a 12-in.-by-12-in. sheet of.

Optimization Problems 1.Identify the quantity you’re optimizing 2.Write an equation for that quantity 3.Identify any constraints, and use them to get the.

Sec 4.7: Optimization Problems EXAMPLE 1 An open-top box is to be made by cutting small congruent squares from the corners of a 12-in.-by-12-in. sheet.

STEPS IN SOLVING OPTIMIZATION PROBLEMS 1.Understand the Problem The first step is to read the problem carefully until it is clearly understood. Ask yourself:

Calculus 3-R-b Review Problems Sections 3-5 to 3-7, 3-9.

3.7 Optimization Problems Buffalo Bill’s Ranch, North Platte, Nebraska Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1999.

Chapter 12 Graphs and the Derivative Abbas Masum.

Sect. 3-7 Optimization.

Aim: How do we solve optimization problems? A rectangular enclosure is constructed using a barn wall as one side and 63 m of fencing for the other three.

Lesson 6: Optimizing Areas and Perimeters

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Honors Calculus 4.8. Optimization.

Calculus I (MAT 145) Dr. Day Wednesday Nov 8, 2017

Calculus I (MAT 145) Dr. Day Friday Nov 10, 2017

Optimization Chapter 4.4.

7. Optimization.

Optimization Problems

More About Optimization

Lesson 4-4: Modeling and Optimization

3.7 Optimization Problems

AP Calculus BC September 29, 2016.

AP Calculus BC September 30, 2016.

Optimization Problems

3.7 Optimization Problems

A farmer has 100m of fencing to attach to a long wall, making a rectangular pen. What is the optimal width of this rectangle to give the pen the largest.

Using Calculus to Solve Optimization Problems

4.7 Optimization Problems.

Graphs of Rational Functions

Sec 4.7: Optimization Problems

4.5 Optimization Problems

3.7 Optimization Problems

Presentation transcript:

Section 4.7

Optimization – the process of finding an optimal value- either a maximum or a minimum under strict conditions Problem Solving Strategy –  1. Assign symbols to all given quantities and quantities to be determined ( make a sketch )  2. Write a primary equation for the quantity that is to be maximized or minimized.  3. Reduce the primary equation to one single independent variable.  4. Determine the domain.  5. Use calculus to find max or min.  6. VERIFY!!

Practice Problems 1. A farmer has 160 ft of fencing to enclose 2 adjacent rectangular pig pens. What dimensions should be used for each pig pen so that the enclosed area will be a minimum? 2. A man wants to plant a rectangular garden along one side of his house, with a picket fence on the other three sides of the garden. Find the dimensions of the largest garden that can be enclosed using 40 feet of fencing.

3. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of the page are to be 1.5 inches, and the margins on the left and right are to 1 inch. What should be the dimensions of the page so that the least amount of paper is used? 4. Which points on the graph are closest to the point (0,2)?