3.7 Optimization Problems

Slides:

Advertisements

Similar presentations

3.7 Modeling and Optimization

Advertisements

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

OPTIMIZATION © Alex Teshon Daffy Durairaj.

Lesson 2-4 Finding Maximums and Minimums of Polynomial Functions.

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

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.

A rectangular dog pen is constructed using a barn wall as one side and 60m of fencing for the other three sides. Find the dimensions of the pen 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.

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

Section 3.7 – Optimization Problems. Optimization Procedure 1.Draw a figure (if appropriate) and label all quantities relevant to the problem. 2.Focus.

Chapter 2 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Quadratic Functions.

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

Section 14.2 Application of Extrema

Section 4.4: Modeling and Optimization

{ ln x for 0 < x < 2 x2 ln 2 for 2 < x < 4 If f(x) =

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) =

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

4.4. Optimization Optimization is one of the most useful applications of the derivative. It is the process of finding when something is at a maximum or.

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.

Optimization Problems

Da Nang-11/2013 Natural Science Department – Duy Tan University Lecturer: Ho Xuan Binh Optimization Problems. In this section, we will learn: How to solve.

Optimization Problems Section 4.5. Find the dimensions of the rectangle with maximum area that can be inscribed in a semicircle of radius 10.

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

Section 4.6/4.7: Optimization Problems Practice HW from Stewart Textbook (not to hand in) p. 311 # 1-13 odd, 19, 21, 24, 33, p. 321 # 9,

Optimization Problems

Constraints Feasible region Bounded/ unbound Vertices

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

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

Copyright © Cengage Learning. All rights reserved. Applications of Differentiation.

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

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:

Optimization Problems. A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along.

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.

Optimization Buffalo Bill’s Ranch, North Platte, Nebraska

Ch. 5 – Applications of Derivatives

Lesson 6: Optimizing Areas and Perimeters

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

2.4 Quadratic Models.

Quadratic Functions.

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.

4.6 Optimization The goal is to maximize or minimize a given quantity subject to a constraint. Must identify the quantity to be optimized – along with.

Lesson 4-4: Modeling and Optimization

AP Calculus BC September 29, 2016.

AP Calculus BC September 30, 2016.

Optimization Problems

Optimization Rizzi – Calc BC.

Using Calculus to Solve Optimization Problems

Optimization (Max/Min)

Day 168 – Cubical and cuboidal structures

3.7 Optimization.

Sec 4.7: Optimization Problems

Calculus I (MAT 145) Dr. Day Wednesday March 27, 2019

Calculus I (MAT 145) Dr. Day Monday April 8, 2019

3.7 Optimization Problems

Optimization (Max/Min)

4.5 Optimization Problems

Presentation transcript:

3.7 Optimization Problems -Determination of minimum and maximum values. -Greatest profit, least cost, least time, greatest voltage, optimum size, least size, greatest distance.

Process Identify your quantities given and quantities to be determined. Write a primary equation for the quantity that needs to be optimized. Reduce the primary equation to one having a single independent variable. May need a secondary equation relating the independent variables of the primary equation. Determine the feasible domain (what values make sense for an answer) Use calculus techniques learned in Ch.3 to find given variables.

A hobby store has 20 ft of fencing to fence off a rectangular area for an electric train in one corner of its display room. The two sides against the wall do not require a fence. What dimensions of the rectangle will maximize the area? What is the maximum area?