The seniors plan to make a smell-proof enclosure for the freshmen using the Northern Parkway wall as one side. If they have 200 yards of fencing, what.

Slides:

Advertisements

Similar presentations

problems on optimization

Advertisements

QUIZ.

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

To optimize something means to maximize or minimize some aspect of it… Strategy for Solving Max-Min Problems 1. Understand the Problem. Read the problem.

3.7 Optimization Problems

Pre – CalcLesson 2.4 Finding Maximums and Minimums of Polynomial Functions For quadratic functions: f(x) = ax 2 + bx + c To fin d the max. or min. 1 st.

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.

Applications of Differentiation

3.4 Quadratic Modeling.

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.

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

Modeling and Optimization

Optimization Practice Problems.

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.

Homework Homework Assignment #27 Review Section 4.6 Page 265, Exercises: 1 – 29 (EOO),19, skip 17 Quiz next time Rogawski Calculus Copyright © 2008 W.

Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Modeling with Functions.

Applications of Maxima and Minima Optimization Problems

Perimeter, Circumference, and Area BIG IDEA: MEASUREMENT ESSENTIAL UNDERSTANDINGS: Perimeter, circumference, and area are different ways of measuring the.

Using Calculus to Solve Optimization Problems

Lesson 4.4 Modeling and Optimization What you’ll learn about Using derivatives for practical applications in finding the maximum and minimum values in.

AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3 1 Expressing a quantity as a function of another quantity. Do Now: Express.

Applied Max and Min Problems Objective: To use the methods of this chapter to solve applied optimization problems.

4.7 Applied Optimization Wed Jan 14

Applied Max and Min Problems

Section 14.2 Application of Extrema

1.Tim is painting his living room with a new coffee colored Paint. There are 3 walls in the living room that measure 15 ft by 8 ft each and a fourth wall.

Linearization , Related Rates, and Optimization

Section 4.4 Optimization and Modeling

Calculus and Analytical Geometry

AP CALCULUS AB Chapter 4: Applications of Derivatives Section 4.4:

QUADRATIC MODELS: BUILDING QUADRATIC FUNCTIONS

PRE-ALGEBRA. Reasoning Strategy: Make a Model (10-8) How can you use a model to help solve a problem? Example: A box company makes boxes to hold popcorn.

Sullivan PreCalculus Section 2.6 Mathematical Models: Constructing Functions Objectives Construct and analyze functions.

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

C2: Maxima and Minima Problems

Theorems I LOVE Parametric Equations Factors, Remainders, And Roots (oh my!) Max-MinInequalitiesGraph.

Extra Optimization Problems “Enrichment Problems”.

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

1. The sum of two nonnegative numbers is 20. Find the numbers

Finding Maximum and Minimum Values. Congruent squares are cut from the corners of a 1m square piece of tin, and the edges are then turned up to make an.

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

Many times in life we are asked to do an optimization problem – that is, find the largest or smallest value of some quantity…  Find the route which will.

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

Formulas: Perimeter of a rectangle: P = 2l + 2w Area of a rectangle : A = lw Perimeter of a square : P = 4s Area of a square: A = s 2 Circumference of.

Make a Model A box company makes boxes to hold popcorn. Each box is made by cutting the square corners out of a rectangular sheet of cardboard. The rectangle.

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

2.7 Mathematical Models Some will win, some will lose, some are born to sing the blues. Oh the movie never ends, it goes on and on and on and on. -Journey.

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.

Building Boxes What is the largest volume open top box that you can build from an 8 ½ by 11 inch sheet of paper?

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

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Maximum-Minimum (Optimization) Problems OBJECTIVE  Solve maximum and minimum.

2.6 Extreme Values of Functions

Optimization Problems

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

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

Ch. 5 – Applications of Derivatives

Lesson 6: Optimizing Areas and Perimeters

MAXIMIZING AREA AND VOLUME

Applied Max and Min Problems

Optimization Chapter 4.4.

Chapter 5: Applications of the Derivative

From a square sheet of paper 20 cm by 20 cm, we can make a box without a lid. We do this by cutting a square from each corner and folding up the flaps.

Optimization (Max/Min)

Chapter 3: Polynomial Functions

6.7 Using the Fundamental Theorem of Algebra

Finding Maximums & Minimums of Polynomial Functions fguilbert.

Presentation transcript:

The seniors plan to make a smell-proof enclosure for the freshmen using the Northern Parkway wall as one side. If they have 200 yards of fencing, what is the largest enclosure they could make? What is the domain of the function?

Coach Gouline plans to build a rectangular pen for Sherman, the official German Shepherd of his house. He plans to use the house as one side of the pen and use 140 feet of fencing to finish the enclosure. What is the largest possible area of Sherman’s grounds?

A capture the flag pitch is a large rectangle with a line dividing it in half. Suppose you have enough paint for 600 feet of lines. What is the largest pitch (by area) you could create?

John plans to dive off a 10-foot tall diving board. He jumps upwards at 20 feet per second. His height as a function of time is given by: h(t)=-16t 2 +20t+10. Find his maximum height and the amount of time he is in the air.

Jack grows corn on his farm. He currently has 500 bushels of corn ready to ship, but he will be able to harvest 15 more bushels for each day that he waits. Right now, corn sells for $82 per bushel, but the price is expected to drop $2 a day. How long should Jack wait to maximize his revenue? What is the domain of the function?

The Organization of the Petroleum Exporting Countries (OPEC) controls nearly 80% of the world’s oil reserves, and largely dictates the price of oil. Currently, OPEC produces approximately 29 million barrels of oil a day and sells each barrel for around $45 dollars per barrel. OPEC estimates that for every million additional barrels they produce, the cost of oil will decrease $1.25. What price of oil will maximize their revenue?

I have a 4 foot by 8 foot piece of sheet metal. I plan to make a box by cutting the corners off the box and folding the sides up. Write the volume of the box, V, as a function of x, the amount cut off each edge. Find the maximum volume. What is the domain of the function?

A cylinder is generated by rotating a rectangle with perimeter 20 around the y-axis. Find the volume of the cylinder as a function of x, the height. What is the domain of the function? Find the maximum volume.

A second cylinder is inscribed in a sphere of radius 10. What is the maximum volume of the cylinder? What is the domain of the function?

I have 100 yards of fencing, and I can either make one square pen or two square pens (that need not be identical). How can I maximize (or minimize) the enclosed area.

I have 300 yards of fencing, and I need to enclose two pens— one for freshmen and one for seniors. How can I maximize the total enclosed area?

Now, I plan to use an identical piece of sheet metal to make a box with a lid. Find V(x) and the maximum volume.