3.3 Optimization Problems Day 1

Slides:

Advertisements

Similar presentations

problems on optimization

Advertisements

3.7 Modeling and Optimization

4.4 Optimization.

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

Optimization 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.

4.7 Applied Optimization Wed Dec 17 Do Now Differentiate 1) A(x) = x(20 - x) 2) f(x) = x^3 - 3x^2 + 6x - 12.

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.

Sheep fencing problems Calculus wall sheep fencing A farmer has a field in which there is a very long straight wall. The farmer also has 340 metres of.

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.

Sec 2.5 – Max/Min Problems – Business and Economics Applications

Modeling and Optimization

Business and Economic Models

4.7 Optimization Problems 1.  In solving such practical problems the greatest challenge is often to convert the word problem into a mathematical optimization.

Applications of Maxima and Minima Optimization Problems

4.7 Applied Optimization Wed Jan 14

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

4.7 Optimization Problems

Calculus and Analytical Geometry

Welcome to... A Game of X’s and O’s

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

4.7 Optimization Problems In this section, we will learn: How to solve problems involving maximization and minimization of factors. APPLICATIONS OF DIFFERENTIATION.

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

Aim: Curve Sketching Do Now: Worksheet Aim: Curve Sketching.

6.2 – Optimization Calculus - Santowski Calculus - Santowski 4/24/2017.

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.

C2: Maxima and Minima Problems

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

5023 MAX - Min: Optimization AP Calculus. OPEN INTERVALS: Find the 1 st Derivative and the Critical Numbers First Derivative Test for Max / Min –TEST.

Optimization Problems

Applied Max and Min Problems (Optimization) 5.5. Procedures for Solving Applied Max and Min Problems 1.Draw and Label a Picture 2.Find a formula for the.

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 –

CHAPTER Continuity Optimization Problems. Steps in Solving Optimizing Problems : 1.Understand the problem. 2.Draw a diagram. 3.Introduce notation.

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.

2.7 Mathematical Models. Optimization Problems 1)Solve the constraint for one of the variables 2)Substitute for the variable in the objective Function.

Physics 2D Motion worksheet Selected question answers.

Chapter 11 Maximum and minimum points and optimisation problems Learning objectives:  Understand what is meant by stationary point  Find maximum and.

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.

6.2: Applications of Extreme Values Objective: To use the derivative and extreme values to solve optimization problems.

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.

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

2.6 Extreme Values of Functions

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

Optimization Problems

EQ: How are extreme values useful in problem solving situations?

Sect. 3-7 Optimization.

Ch. 5 – Applications of Derivatives

Lesson 6: Optimizing Areas and Perimeters

MAXIMIZING AREA AND VOLUME

12,983 {image} 12,959 {image} 12,960 {image} 12,980 {image}

Optimization Chapter 4.4.

7. Optimization.

Chapter 5: Applications of the Derivative

Optimization Problems

3.7 Optimization Problems

4.7 Optimization Problems.

At what point is the following function a local minimum? {image}

4.6 Optimization Problems

3.7 Optimization.

Sec 4.7: Optimization Problems

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

3.7 Optimization Problems

3/7/15 LESSON 43 –APPLICATIONS OF DERIVATIVES – Motion, Related Rates and Optimization – DAY 4 IBHL1 - Calculus - Santowski Math HL1 - Santowski.

Presentation transcript:

3.3 Optimization Problems Day 1

Example #1: Optimal Area A farmer has 800 m of fencing and wishes to enclose a rectangular field. One side of the field is against a country road that is already fenced, so the farmer needs to fence only the remaining three sides of the field. If the farmer uses all of the fencing provided, what is the maximum area that he can enclose? What dimensions produce this area?

Example #2: Optimal Volume A piece of sheet metal, 60cm by 30 cm, is to be used to make a rectangular box with an open top. Determine the dimensions that will give the box the largest volume.

Example #3: Minimizing Distance Ian and Ada are both training for a marathon. Ian’s house is located 20 km north of Ada’s house. At 9:00 am one Saturday, Ian leaves his house and jogs south at 8 km/h. At the same time, Ada leaves her house and jogs east at 6 km/h. When are Ian and Ada closest together, given that they both run for 2.5 h.

QUESTIONS: p.145-147 #4, 8, 10, 11, 15, 19b, 20