Optimization. A company manufactures and sells x videophones per week. The weekly price-demand and cost equations are What price should the company charge.

Slides:



Advertisements
Similar presentations
Maxima and Minima in Plane and Solid Figures
Advertisements

Guidelines for Solving Applied Minimum and Maximum Problems 1.Identify all given quantities and quantities to be determined. If possible, make a sketch.
QUIZ.
Rod cutting Decide where to cut steel rods:
Standard  MM3A6. Students will solve linear programming problems in two variables.  a. Solve systems of inequalities in two variables, showing the solutions.
Optimization Problems
3.7 Optimization Problems
Section 4.5 The Derivative in Graphing and Applications: “Applied Maximum and Minimum Problems”
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.
Polynomial Functions Section 2.3. Objectives Find the x-intercepts and y-intercept of a polynomial function. Describe the end behaviors of a polynomial.
Example 2 Finding the Maximum Volume Chapter 6.3 A box is to be formed by cutting squares x inches per side from each corner of a square piece of cardboard.
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.

1 Applications of Extrema OBJECTIVE  Solve maximum and minimum problems using calculus. 6.2.
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.
Sec 2.5 – Max/Min Problems – Business and Economics Applications
Quick Quiz True or False
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.
Applied Max and Min Problems Objective: To use the methods of this chapter to solve applied optimization problems.
Applied Max and Min Problems
Section 14.2 Application of Extrema
2.5 Copyright © 2014 Pearson Education, Inc. Maximum-Minimum Problems; Business and Economics Applications OBJECTIVE Solve maximum and minimum problems.
Sec 4.5 – Indeterminate Forms and L’Hopital’s Rule Indeterminate Forms L’Hopital’s Rule.
Applications Involving Inequalities
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.
Optimization. Objective  To solve applications of optimization problems  TS: Making decisions after reflection and review.
Sullivan PreCalculus Section 2.6 Mathematical Models: Constructing Functions Objectives Construct and analyze functions.
OPTIMIZATION.
Chapter 5 Graphing and Optimization Section 6 Optimization.
Notes Over 6.8 Using x-Intercepts to Graph a Polynomial Function Graph the function. x-inter: 1, -2 End behavior: degree 3 L C: positive Bounces off of.
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
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.
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.
MTH 251 – Differential Calculus Chapter 4 – Applications of Derivatives Section 4.6 Applied Optimization Copyright © 2010 by Ron Wallace, all rights reserved.
Optimization. First Derivative Test Method for finding maximum and minimum points on a function has many practical applications called Optimization -
5.2 Properties of Parabolas Word Problems. Word Problems p.247 Quick Check The number of widgets the Woodget Company sells can be modeled by -5p + 100,
Precalculus Section 2.4 Use polynomials to find maximum and minimum values Example 1 page 69 Area = length x width A(x) = (60 – 2x)(x) A(x) = 60x - 2x².
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 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.
A25 & 26-Optimization (max & min problems). Guidelines for Solving Applied Minimum and Maximum Problems 1.Identify all given quantities and quantities.
Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Building Boxes What is the largest volume open top box that you can build from an 8 ½ by 11 inch sheet of paper?
1.9 and 1.10 Converting from General to Standard Forms of Circles Modeling with Functions Pg. 240 # even (You do NOT have to graph these) Pg. 251.
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.
3.7 Optimization Problems Buffalo Bill’s Ranch, North Platte, Nebraska Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1999.
Maximum Volume of a Box An Investigation Maximum volume of a box From a square piece of cardboard of side 20 cm small corners of side x are cut off.
EQ: How are extreme values useful in problem solving situations?
Chapter 12 Graphing and Optimization
Optimization Cont..
Maximum-Minimum Problems; Business and Economics Applications
A car rental agency charges $200 per week plus $0
Choose the Best Regression Equation
MAXIMIZING AREA AND VOLUME
Applied Max and Min Problems
Optimization Chapter 4.4.
Bellwork You are making a rectangular box out of a 16-inch-by-20- inch piece of cardboard. The box will be formed by making the cuts shown in the diagram.
3.6 Mathematical Models: Constructing Functions
3.7 Optimization Problems
2.7 Mathematical Models: Constructing Functions
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 Rizzi – Calc BC.
Optimization (Max/Min)
5.4 Modeling and Optimization
2.7 Mathematical Models: Constructing Functions
6.7 Using the Fundamental Theorem of Algebra
Optimization (Max/Min)
3.7 Optimization Problems
Presentation transcript:

Optimization

A company manufactures and sells x videophones per week. The weekly price-demand and cost equations are What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue? What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit?

A company manufactures and sells x videophones per week. The weekly price-demand and cost equations are What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue?

What is the maximum weekly profit? What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? 500 phones, $250 each A company manufactures and sells x videophones per week. The weekly price-demand and cost equations are What is the maximum weekly revenue? What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit?

What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? 500 phones, $250 each A company manufactures and sells x videophones per week. The weekly price-demand and cost equations are What is the maximum weekly revenue?

What is the maximum weekly revenue? $125,000 What is the maximum weekly profit? What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? 500 phones, $250 each A company manufactures and sells x videophones per week. The weekly price-demand and cost equations are What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit?

What is the maximum weekly revenue? $125,000 What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? 500 phones, $250 each A company manufactures and sells x videophones per week. The weekly price-demand and cost equations are What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit?

What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? 365 phones, $ each What is the maximum weekly revenue? $125,000 What is the maximum weekly profit? What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? 500 phones, $250 each A company manufactures and sells x videophones per week. The weekly price-demand and cost equations are

What is the maximum weekly profit? $46, What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? 365 phones, $ each What is the maximum weekly revenue? $125,000 What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? 500 phones, $250 each A company manufactures and sells x videophones per week. The weekly price-demand and cost equations are

A publishing company sells 50,000 copies of a certain book each year. It costs the company $1 to store a book for 1 year. Each time that it prints additional copies, it costs the company $1000 to set up the presses. How many books should the company produce during each printing, and how many times a year should they print, in order to minimize the total inventory costs? Total inventory costSet-up costStorage cost _____ Books per run_____ runs per year

A publishing company sells 50,000 copies of a certain book each year. It costs the company $1 to store a book for 1 year. Each time that it prints additional copies, it costs the company $1000 to set up the presses. How many books should the company produce during each printing, and how many times a year should they print, in order to minimize the total inventory costs? Total inventory costSet-up costStorage cost _____ Books per run_____ runs per year

A publishing company sells 50,000 copies of a certain book each year. It costs the company $1 to store a book for 1 year. Each time that it prints additional copies, it costs the company $1000 to set up the presses. How many books should the company produce during each printing, and how many times a year should they print, in order to minimize the total inventory costs? Total inventory costSet-up costStorage cost _____ Books per run_____ runs per year

A publishing company sells 50,000 copies of a certain book each year. It costs the company $1 to store a book for 1 year. Each time that it prints additional copies, it costs the company $1000 to set up the presses. How many books should the company produce during each printing, and how many times a year should they print, in order to minimize the total inventory costs? _____ Books per run_____ runs per year

A publishing company sells 50,000 copies of a certain book each year. It costs the company $1 to store a book for 1 year. Each time that it prints additional copies, it costs the company $1000 to set up the presses. How many books should the company produce during each printing, and how many times a year should they print, in order to minimize the total inventory costs? _____ Books per run_____ runs per year 10,000 books each printing5 printings per year

A box is to be made from a piece of cardboard that measures 10 inches by 12 inches Squares will be cut from each corner.The sides will be folded up to form a rectangular box.What size squares should be cut from each corner to obtain maximum volume? ? ? ? ? Work it on your paper.