Sec 3.5 Business and Economics Applications. Solution step1 sketch the function. step 2 The primary equation is
|
|
- Randell Foster
- 7 years ago
- Views:
Transcription
1 Sec 3.5 Business and Economics Applications rev0216 Objectives: 1. Solve business and economics optimization problems 2. Find the price elasticity of demand for demand functions. 3. Recognize basic business terms and formulas - Eample 1: Finding the Maimum Revenue A company has determined that its total revenue (dollars) for a product can be modeled by R where number of units produced (and sold). What production level will yield a maimum revenue Solution step1 sketch the function R y 3e+7 2e+7 1e step 2 The primary equation is R step 3- R is a function on 1 variable No other equation is necessary step 4 -Determine feasible domain When R zero from the equation , Solution is: , positive value Also from the graph appro 550 step 5- maimize the revenue R dr d , 350 units step 6- statement The production level of 350 units will maimize the revenue Definition: Average cost C C 1
2 Eample 2. Finding the minimum Average Cost A company estimates that the cost (dollars) of producing units of product can be modeled by C Find the production level that minimizes the average cost per unit Solution step1 define and sketch (if practical) the function C average cost C C step 2 The primary equation is C step 3- C is already a function on 1 variable no secondary equation required step 4 -Determine feasible domain 0 step 5- mimize the average cost C dc , d , Solution is: 2000, units step 6- statement The production level of 2000 units will minimize the average cost - Do NOW check point 1 Maimize Revenue R Don t need to sketch Given primary equation R 4. Find feasible domain R 0 and solve for where 0 5. Maimize R to find the number of units 6. Statement Asked: What is the maimum revenue? Find revenue for value found in 5. Eample 3 Finding the Maimum Revenue A business sells 2000 units of a product per month at a price of $10 each It can sell 250 more items per month for each $0.25 reduction in price. What price per unit will maimize the monthly revenue? step 1. number of units sold / mo 2
3 p price per unit R monthly revenue step 2 R p primary equation Note: usually the equation for p is given. Here we have to compute it step 3 p $10 means 2000 units p $ units To get the formula for p, use point slope formula change in price p slope m change in p p secondary equation R p primary equation step 4 feasible domain 0 Where is the R 0 ans: 0 and step 5 maimize revenue- find critical number R dr d 6000 units step 6 statement: What were we asked to find? What price per unit will maimize the monthly revenue? p p $6. 0 Production level which maimizes revenue corresponds to a price of $6 per unit Eample 4 Maimum Profit The marketing department of a business has determined the demand for a product can be modeled by p 50 The cost of producting units is given by C What price will yield a maimum profit? step 1 R p, revenue function step 2 P profit R C primary equation 3
4 step 3 R p secondary equation P R C P step4 feasible domain Want possible profit solve radical equation for or graph and estimate the domain step5 maimize P P dp , d Solution is: units. step 6 statement What were we asked? What price will yield a maimum profit? p When is 2500 units, profit is maimized. This corresponds to a selling price of $ 1 per unit. Do NOW # 9 sec Form R p, secondary equation 3. Form primary equation P R C 4. Find feasible domain P 0 and solve for where 0 5. Maimize P to find the number of units 6. Statement What is the price that will maimize profit? Substitute in p and solve for. Look at price elasticity of Demand together. - Price Elasticity of Demand A drop in price might create greater demand for product and thus more Revenue For eample, lowering the price of fresh tomatoes results in selling more tomatoes and is sufficient to increase the revenue. We say the demand is elastic A drop in price might NOT create greater demand and the Revenue might actually decrease. For eample lowering the price of gasoline or coffee might NOT result in greater demand and might NOT be sufficient to increase revenue. We say the demand is inelastic. (not too sensitive to changes in price) 4
5 rate of change of demand Thus price elasticity of demand, rate of change in price is the lower case greek letter, eta Let quantity demanded p price of item rate of change of demand rate of change in price / p/p p/ p/ price elasticity of demand is p/ is lower case greek letter, eta dp/d For a given price, and R revenue function The demand is elastic if 1 dr d 0 R increasing The demand is inelastic if 1 dr d 0 R decreasing Eample 5 Comparing Elasticity and Revenue The demand function for a product is modeled by p 24 2 y a. Find the intervals on which the demand is elastic, inelcastic,and of unit elasticity - p/ dp/d unit elasticity Recall the definition of absolute value c c is equivalent to ( c or c) solving Solution gives
6 solving where the function is defined so chose 144 gives 64, in the domain or This divides the domain into 2 regions 0, 64 and 64, 144 Test a point in each region to determine if 1 or 1 table region 0, 64 64, 144 test value when 0 64 elastic demand 1 when inelastic demand - b. Use the result of part a to describe the behavior of the revenue function R is increasing 1 when 0 64 and R is increasing R is decreasing 1 when and R is decreasing - R is a maimum at 64 units because it changes from increasing to deareasing here R p R R y Do NOW (if time) check point
7 7
Business and Economic Applications
Appendi F Business and Economic Applications F1 F Business and Economic Applications Understand basic business terms and formulas, determine marginal revenues, costs and profits, find demand functions,
More informationSection 3-7. Marginal Analysis in Business and Economics. Marginal Cost, Revenue, and Profit. 202 Chapter 3 The Derivative
202 Chapter 3 The Derivative Section 3-7 Marginal Analysis in Business and Economics Marginal Cost, Revenue, and Profit Application Marginal Average Cost, Revenue, and Profit Marginal Cost, Revenue, and
More informationSection 7.2 Linear Programming: The Graphical Method
Section 7.2 Linear Programming: The Graphical Method Man problems in business, science, and economics involve finding the optimal value of a function (for instance, the maimum value of the profit function
More informationElasticity. I. What is Elasticity?
Elasticity I. What is Elasticity? The purpose of this section is to develop some general rules about elasticity, which may them be applied to the four different specific types of elasticity discussed in
More information3.3 Applications of Linear Functions
3.3 Applications of Linear Functions A function f is a linear function if The graph of a linear function is a line with slope m and y-intercept b. The rate of change of a linear function is the slope m.
More informationSolutions of Equations in Two Variables
6.1 Solutions of Equations in Two Variables 6.1 OBJECTIVES 1. Find solutions for an equation in two variables 2. Use ordered pair notation to write solutions for equations in two variables We discussed
More informationLecture 2. Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization
Lecture 2. Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization 2.1. Introduction Suppose that an economic relationship can be described by a real-valued
More informationElasticity. Demand is inelastic if it does not respond much to price changes, and elastic if demand changes a lot when the price changes.
Elasticity The price elasticity of demand measures the sensitivity of the quantity demanded to changes in the price. Demand is inelastic if it does not respond much to price changes, and elastic if demand
More information1 Calculus of Several Variables
1 Calculus of Several Variables Reading: [Simon], Chapter 14, p. 300-31. 1.1 Partial Derivatives Let f : R n R. Then for each x i at each point x 0 = (x 0 1,..., x 0 n) the ith partial derivative is defined
More informationSolving Quadratic Equations by Graphing. Consider an equation of the form. y ax 2 bx c a 0. In an equation of the form
SECTION 11.3 Solving Quadratic Equations b Graphing 11.3 OBJECTIVES 1. Find an ais of smmetr 2. Find a verte 3. Graph a parabola 4. Solve quadratic equations b graphing 5. Solve an application involving
More informationDemand, Supply and Elasticity
Demand, Supply and Elasticity CHAPTER 2 OUTLINE 2.1 Demand and Supply Definitions, Determinants and Disturbances 2.2 The Market Mechanism 2.3 Changes in Market Equilibrium 2.4 Elasticities of Supply and
More informationUtility Maximization
Utility Maimization Given the consumer's income, M, and prices, p and p y, the consumer's problem is to choose the a ordable bundle that maimizes her utility. The feasible set (budget set): total ependiture
More information1 Maximizing pro ts when marginal costs are increasing
BEE12 Basic Mathematical Economics Week 1, Lecture Tuesda 12.1. Pro t maimization 1 Maimizing pro ts when marginal costs are increasing We consider in this section a rm in a perfectl competitive market
More information1.6. Piecewise Functions. LEARN ABOUT the Math. Representing the problem using a graphical model
1.6 Piecewise Functions YOU WILL NEED graph paper graphing calculator GOAL Understand, interpret, and graph situations that are described by piecewise functions. LEARN ABOUT the Math A city parking lot
More information1 Economic Application of Derivatives
1 Economic Application of Derivatives deriv-applic.te and.pdf April 5, 2007 In earlier notes, we have already considered marginal cost as the derivative of the cost function. That is mc() = c 0 () How
More informationPricing I: Linear Demand
Pricing I: Linear Demand This module covers the relationships between price and quantity, maximum willing to buy, maximum reservation price, profit maximizing price, and price elasticity, assuming a linear
More information2.7 Applications of Derivatives to Business
80 CHAPTER 2 Applications of the Derivative 2.7 Applications of Derivatives to Business and Economics Cost = C() In recent ears, economic decision making has become more and more mathematicall oriented.
More informationSection 2.5 Average Rate of Change
Section.5 Average Rate of Change Suppose that the revenue realized on the sale of a company s product can be modeled by the function R( x) 600x 0.3x, where x is the number of units sold and R( x ) is given
More informationFunctions: Piecewise, Even and Odd.
Functions: Piecewise, Even and Odd. MA161/MA1161: Semester 1 Calculus. Prof. Götz Pfeiffer School of Mathematics, Statistics and Applied Mathematics NUI Galway September 21-22, 2015 Tutorials, Online Homework.
More information1 Mathematical Models of Cost, Revenue and Profit
Section 1.: Mathematical Modeling Math 14 Business Mathematics II Minh Kha Goals: to understand what a mathematical model is, and some of its examples in business. Definition 0.1. Mathematical Modeling
More informationSuppose you are a seller with cost 13 who must pay a sales tax of 15. What is the lowest price you can sell at and not lose money?
Experiment 3 Suppose that sellers pay a tax of 15. If a seller with cost 5 sells to a buyer with value 45 at a price of 25, the seller earns a profit of and the buyer earns a profit of. Suppose you are
More informationAverage rate of change of y = f(x) with respect to x as x changes from a to a + h:
L15-1 Lecture 15: Section 3.4 Definition of the Derivative Recall the following from Lecture 14: For function y = f(x), the average rate of change of y with respect to x as x changes from a to b (on [a,
More informationMarginal Cost. Example 1: Suppose the total cost in dollars per week by ABC Corporation for 2
Math 114 Marginal Functions in Economics Marginal Cost Suppose a business owner is operating a plant that manufactures a certain product at a known level. Sometimes the business owner will want to know
More information14.01 Fall 2010 Problem Set 1 Solutions
14.01 Fall 2010 Problem Set 1 Solutions 1. (25 points) For each of the following scenarios, use a supply and demand diagram to illustrate the effect of the given shock on the equilibrium price and quantity
More informationSolving Quadratic Equations
9.3 Solving Quadratic Equations by Using the Quadratic Formula 9.3 OBJECTIVES 1. Solve a quadratic equation by using the quadratic formula 2. Determine the nature of the solutions of a quadratic equation
More informationWhy should we learn this? One real-world connection is to find the rate of change in an airplane s altitude. The Slope of a Line VOCABULARY
Wh should we learn this? The Slope of a Line Objectives: To find slope of a line given two points, and to graph a line using the slope and the -intercept. One real-world connection is to find the rate
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MBA 640 Survey of Microeconomics Fall 2006, Quiz 6 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A monopoly is best defined as a firm that
More informationElasticities of Demand and Supply
1 CHAPTER CHECKLIST Elasticities of Demand and Supply Chapter 5 1. Define, explain the factors that influence, and calculate the price elasticity of demand. 2. Define, explain the factors that influence,
More information0 0 such that f x L whenever x a
Epsilon-Delta Definition of the Limit Few statements in elementary mathematics appear as cryptic as the one defining the limit of a function f() at the point = a, 0 0 such that f L whenever a Translation:
More informationSupply and Demand Fundamental tool of economic analysis Used to discuss unemployment, value of $, protection of the environment, etc.
Supply and emand Fundamental tool of economic analysis Used to discuss unemployment, value of $, protection of the environment, etc. Chapter Outline: (a) emand is the consumer side of the market. (b) Supply
More informationMA107 Precalculus Algebra Exam 2 Review Solutions
MA107 Precalculus Algebra Exam 2 Review Solutions February 24, 2008 1. The following demand equation models the number of units sold, x, of a product as a function of price, p. x = 4p + 200 a. Please write
More information, plus the present value of the $1,000 received in 15 years, which is 1, 000(1 + i) 30. Hence the present value of the bond is = 1000 ;
2 Bond Prices A bond is a security which offers semi-annual* interest payments, at a rate r, for a fixed period of time, followed by a return of capital Suppose you purchase a $,000 utility bond, freshly
More informationSolutions to Quadratic Equations Word Problems
Area Problems: Solutions to Quadratic Equations Word Problems 9. A local building code requires that all factories must be surrounded by a lawn. The width of the lawn must be uniform and the area must
More informationSolving Systems of Equations
Solving Sstems of Equations When we have or more equations and or more unknowns, we use a sstem of equations to find the solution. Definition: A solution of a sstem of equations is an ordered pair that
More informationCore Maths C3. Revision Notes
Core Maths C Revision Notes October 0 Core Maths C Algebraic fractions... Cancelling common factors... Multipling and dividing fractions... Adding and subtracting fractions... Equations... 4 Functions...
More informationAP Microeconomics Chapter 12 Outline
I. Learning Objectives In this chapter students will learn: A. The significance of resource pricing. B. How the marginal revenue productivity of a resource relates to a firm s demand for that resource.
More informationElasticity: The Responsiveness of Demand and Supply
Chapter 6 Elasticity: The Responsiveness of Demand and Supply Chapter Outline 61 LEARNING OBJECTIVE 61 The Price Elasticity of Demand and Its Measurement Learning Objective 1 Define the price elasticity
More informationElasticity and Its Application
Elasticity and Its Application Chapter 5 All rights reserved. Copyright 2001 by Harcourt, Inc. Requests for permission to make copies of any part of the work should be mailed to: Permissions Department,
More informationChapter 6. Elasticity: The Responsiveness of Demand and Supply
Chapter 6. Elasticity: The Responsiveness of Demand and Supply Instructor: JINKOOK LEE Department of Economics / Texas A&M University ECON 202 504 Principles of Microeconomics Elasticity Demand curve:
More informationMAT12X Intermediate Algebra
MAT12X Intermediate Algebra Workshop I - Exponential Functions LEARNING CENTER Overview Workshop I Exponential Functions of the form y = ab x Properties of the increasing and decreasing exponential functions
More informationAlgebra II A Final Exam
Algebra II A Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. Evaluate the expression for the given value of the variable(s). 1. ; x = 4 a. 34 b.
More informationPre-Test Chapter 18 ed17
Pre-Test Chapter 18 ed17 Multiple Choice Questions 1. (Consider This) Elastic demand is analogous to a and inelastic demand to a. A. normal wrench; socket wrench B. Ace bandage; firm rubber tie-down C.
More informationStudent Activity: To investigate an ESB bill
Student Activity: To investigate an ESB bill Use in connection with the interactive file, ESB Bill, on the Student s CD. 1. What are the 2 main costs that contribute to your ESB bill? 2. a. Complete the
More informationM122 College Algebra Review for Final Exam
M122 College Algebra Review for Final Eam Revised Fall 2007 for College Algebra in Contet All answers should include our work (this could be a written eplanation of the result, a graph with the relevant
More informationAbsolute Value Equations and Inequalities
. Absolute Value Equations and Inequalities. OBJECTIVES 1. Solve an absolute value equation in one variable. Solve an absolute value inequality in one variable NOTE Technically we mean the distance between
More informationELASTICITY Microeconomics in Context (Goodwin, et al.), 3 rd Edition
Chapter 4 ELASTICITY Microeconomics in Context (Goodwin, et al.), 3 rd Edition Chapter Overview This chapter continues dealing with the demand and supply curves we learned about in Chapter 3. You will
More informationSection 1-4 Functions: Graphs and Properties
44 1 FUNCTIONS AND GRAPHS I(r). 2.7r where r represents R & D ependitures. (A) Complete the following table. Round values of I(r) to one decimal place. r (R & D) Net income I(r).66 1.2.7 1..8 1.8.99 2.1
More informationOVERVIEW. 2. If demand is vertical, demand is perfectly inelastic. Every change in price brings no change in quantity.
7 PRICE ELASTICITY OVERVIEW 1. The elasticity of demand measures the responsiveness of 1 the buyer to a change in price. The coefficient of price elasticity is the percentage change in quantity divided
More information8 Polynomials Worksheet
8 Polynomials Worksheet Concepts: Quadratic Functions The Definition of a Quadratic Function Graphs of Quadratic Functions - Parabolas Vertex Absolute Maximum or Absolute Minimum Transforming the Graph
More informationPractice Questions Week 3 Day 1
Practice Questions Week 3 Day 1 Figure 4-1 Quantity Demanded $ 2 18 3 $ 4 14 4 $ 6 10 5 $ 8 6 6 $10 2 8 Price Per Pair Quantity Supplied 1. Figure 4-1 shows the supply and demand for socks. If a price
More informationSection 2-3 Quadratic Functions
118 2 LINEAR AND QUADRATIC FUNCTIONS 71. Celsius/Fahrenheit. A formula for converting Celsius degrees to Fahrenheit degrees is given by the linear function 9 F 32 C Determine to the nearest degree the
More informationCHAPTER 2 THE BASICS OF SUPPLY AND DEMAND
CHAPTER 2 THE BASICS OF SUPPLY AN EMAN EXERCISES 1. Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows: Price ($) emand (millions)
More informationPOLYNOMIAL FUNCTIONS
POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a
More informationIOWA End-of-Course Assessment Programs. Released Items ALGEBRA I. Copyright 2010 by The University of Iowa.
IOWA End-of-Course Assessment Programs Released Items Copyright 2010 by The University of Iowa. ALGEBRA I 1 Sally works as a car salesperson and earns a monthly salary of $2,000. She also earns $500 for
More information1.6. Piecewise Functions. LEARN ABOUT the Math. Representing the problem using a graphical model
1. Piecewise Functions YOU WILL NEED graph paper graphing calculator GOAL Understand, interpret, and graph situations that are described b piecewise functions. LEARN ABOUT the Math A cit parking lot uses
More informationMicroeconomics Sept. 16, 2010 NOTES ON CALCULUS AND UTILITY FUNCTIONS
DUSP 11.203 Frank Levy Microeconomics Sept. 16, 2010 NOTES ON CALCULUS AND UTILITY FUNCTIONS These notes have three purposes: 1) To explain why some simple calculus formulae are useful in understanding
More informationPre-Test Chapter 25 ed17
Pre-Test Chapter 25 ed17 Multiple Choice Questions 1. Refer to the above graph. An increase in the quantity of labor demanded (as distinct from an increase in demand) is shown by the: A. shift from labor
More informationHomework 1 1. Calculus. Homework 1 Due Date: September 26 (Wednesday) 60 1.75x 220 270 160 x 280. R = 115.95x. C = 95x + 750.
Homework 1 1 Calculus Homework 1 Due Date: September 26 (Wednesday) 1. A doughnut shop sells a dozen doughnuts for $4.50. Beyond the fixed cost of $220 per day, it costs $2.75 for enough materials and
More informationChapter 4 One Dimensional Kinematics
Chapter 4 One Dimensional Kinematics 41 Introduction 1 4 Position, Time Interval, Displacement 41 Position 4 Time Interval 43 Displacement 43 Velocity 3 431 Average Velocity 3 433 Instantaneous Velocity
More informationMATH 185 CHAPTER 2 REVIEW
NAME MATH 18 CHAPTER REVIEW Use the slope and -intercept to graph the linear function. 1. F() = 4 - - Objective: (.1) Graph a Linear Function Determine whether the given function is linear or nonlinear..
More informationN. Gregory Mankiw Principles of Economics. Chapter 15. MONOPOLY
N. Gregory Mankiw Principles of Economics Chapter 15. MONOPOLY Solutions to Problems and Applications 1. The following table shows revenue, costs, and profits, where quantities are in thousands, and total
More informationThe Point-Slope Form
7. The Point-Slope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope
More informationAlgebra I. In this technological age, mathematics is more important than ever. When students
In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,
More information2.5 Library of Functions; Piecewise-defined Functions
SECTION.5 Librar of Functions; Piecewise-defined Functions 07.5 Librar of Functions; Piecewise-defined Functions PREPARING FOR THIS SECTION Before getting started, review the following: Intercepts (Section.,
More informationSection 6-3 Double-Angle and Half-Angle Identities
6-3 Double-Angle and Half-Angle Identities 47 Section 6-3 Double-Angle and Half-Angle Identities Double-Angle Identities Half-Angle Identities This section develops another important set of identities
More informationLinear Equations and Inequalities
Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109 - Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................
More informationor, put slightly differently, the profit maximizing condition is for marginal revenue to equal marginal cost:
Chapter 9 Lecture Notes 1 Economics 35: Intermediate Microeconomics Notes and Sample Questions Chapter 9: Profit Maximization Profit Maximization The basic assumption here is that firms are profit maximizing.
More informationMath 120 Final Exam Practice Problems, Form: A
Math 120 Final Exam Practice Problems, Form: A Name: While every attempt was made to be complete in the types of problems given below, we make no guarantees about the completeness of the problems. Specifically,
More informationExponential Functions. Exponential Functions and Their Graphs. Example 2. Example 1. Example 3. Graphs of Exponential Functions 9/17/2014
Eponential Functions Eponential Functions and Their Graphs Precalculus.1 Eample 1 Use a calculator to evaluate each function at the indicated value of. a) f ( ) 8 = Eample In the same coordinate place,
More information1.4 Linear Models. Cost, Revenue, and Profit Functions. Example 1 Linear Cost Function
16314_02_ch1_p033-112.qxd 7/17/06 4:10 PM Page 66 66 Chapter 1 Functions and Linear Models 77. If y and x are related by the linear expression y = mx + b, how will y change as x changes if m is positive?
More informationCHAPTER 5 WORKING WITH SUPPLY AND DEMAND Microeconomics in Context (Goodwin, et al.), 2 nd Edition
CHAPTER 5 WORKING WITH SUPPLY AND DEMAND Microeconomics in Context (Goodwin, et al.), 2 nd Edition Chapter Overview This chapter continues dealing with the demand and supply curves we learned about in
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More informationAlgebra 2. Linear Functions as Models Unit 2.5. Name:
Algebra 2 Linear Functions as Models Unit 2.5 Name: 1 2 Name: Sec 4.4 Evaluating Linear Functions FORM A FORM B y = 5x 3 f (x) = 5x 3 Find y when x = 2 Find f (2). y = 5x 3 f (x) = 5x 3 y = 5(2) 3 f (2)
More informationDerivatives as Rates of Change
Derivatives as Rates of Change One-Dimensional Motion An object moving in a straight line For an object moving in more complicated ways, consider the motion of the object in just one of the three dimensions
More informationWeek 1: Functions and Equations
Week 1: Functions and Equations Goals: Review functions Introduce modeling using linear and quadratic functions Solving equations and systems Suggested Textbook Readings: Chapter 2: 2.1-2.2, and Chapter
More informationAlgebra. Exponents. Absolute Value. Simplify each of the following as much as possible. 2x y x + y y. xxx 3. x x x xx x. 1. Evaluate 5 and 123
Algebra Eponents Simplify each of the following as much as possible. 1 4 9 4 y + y y. 1 5. 1 5 4. y + y 4 5 6 5. + 1 4 9 10 1 7 9 0 Absolute Value Evaluate 5 and 1. Eliminate the absolute value bars from
More information1 Functions, Graphs and Limits
1 Functions, Graphs and Limits 1.1 The Cartesian Plane In this course we will be dealing a lot with the Cartesian plane (also called the xy-plane), so this section should serve as a review of it and its
More informationChapter 9. Systems of Linear Equations
Chapter 9. Systems of Linear Equations 9.1. Solve Systems of Linear Equations by Graphing KYOTE Standards: CR 21; CA 13 In this section we discuss how to solve systems of two linear equations in two variables
More informationSUPPLY AND DEMAND : HOW MARKETS WORK
SUPPLY AND DEMAND : HOW MARKETS WORK Chapter 4 : The Market Forces of and and demand are the two words that economists use most often. and demand are the forces that make market economies work. Modern
More informationMonopoly and Monopsony Labor Market Behavior
Monopoly and Monopsony abor Market Behavior 1 Introduction For the purposes of this handout, let s assume that firms operate in just two markets: the market for their product where they are a seller) and
More informationExample 1: Suppose the demand function is p = 50 2q, and the supply function is p = 10 + 3q. a) Find the equilibrium point b) Sketch a graph
The Effect of Taxes on Equilibrium Example 1: Suppose the demand function is p = 50 2q, and the supply function is p = 10 + 3q. a) Find the equilibrium point b) Sketch a graph Solution to part a: Set the
More informationax 2 by 2 cxy dx ey f 0 The Distance Formula The distance d between two points (x 1, y 1 ) and (x 2, y 2 ) is given by d (x 2 x 1 )
SECTION 1. The Circle 1. OBJECTIVES The second conic section we look at is the circle. The circle can be described b using the standard form for a conic section, 1. Identif the graph of an equation as
More information135 Final Review. Determine whether the graph is symmetric with respect to the x-axis, the y-axis, and/or the origin.
13 Final Review Find the distance d(p1, P2) between the points P1 and P2. 1) P1 = (, -6); P2 = (7, -2) 2 12 2 12 3 Determine whether the graph is smmetric with respect to the -ais, the -ais, and/or the
More informationPrice Elasticity of Demand MATH 104 and MATH 184 Mark Mac Lean (with assistance from Patrick Chan) 2011W
Price Elasticity of Demand MATH 104 and MATH 184 Mark Mac Lean (with assistance from Patrick Chan) 2011W The rice elasticity of demand (which is often shortened to demand elasticity) is defined to be the
More informationElasticity. Ratio of Percentage Changes. Elasticity and Its Application. Price Elasticity of Demand. Price Elasticity of Demand. Elasticity...
Elasticity and Its Application Chapter 5 All rights reserved. Copyright 21 by Harcourt, Inc. Requests for permission to make copies of any part of the work should be mailed to: Permissions Department,
More information0.4 FACTORING POLYNOMIALS
36_.qxd /3/5 :9 AM Page -9 SECTION. Factoring Polynomials -9. FACTORING POLYNOMIALS Use special products and factorization techniques to factor polynomials. Find the domains of radical expressions. Use
More information5.2 Inverse Functions
78 Further Topics in Functions. Inverse Functions Thinking of a function as a process like we did in Section., in this section we seek another function which might reverse that process. As in real life,
More information5.1 Radical Notation and Rational Exponents
Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots
More informationECON 103, 2008-2 ANSWERS TO HOME WORK ASSIGNMENTS
ECON 103, 2008-2 ANSWERS TO HOME WORK ASSIGNMENTS Due the Week of June 23 Chapter 8 WRITE [4] Use the demand schedule that follows to calculate total revenue and marginal revenue at each quantity. Plot
More informationLecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20
Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding
More informationEcon 201 Lecture 8. Price Elasticity of Demand A measure of the responsiveness of quantity demanded to changes in price.
Econ 01 Lecture 8 rice Elasticity of emand measure of the responsiveness of quantity demanded to changes in price. Highly responsive = "elastic" Highly unresponsive = "inelastic" rice elasticity of demand
More informationThis is a square root. The number under the radical is 9. (An asterisk * means multiply.)
Page of Review of Radical Expressions and Equations Skills involving radicals can be divided into the following groups: Evaluate square roots or higher order roots. Simplify radical expressions. Rationalize
More informationa. Meaning: The amount (as a percentage of total) that quantity demanded changes as price changes. b. Factors that make demand more price elastic
Things to know about elasticity. 1. Price elasticity of demand a. Meaning: The amount (as a percentage of total) that quantity demanded changes as price changes. b. Factors that make demand more price
More information3.2. Solving quadratic equations. Introduction. Prerequisites. Learning Outcomes. Learning Style
Solving quadratic equations 3.2 Introduction A quadratic equation is one which can be written in the form ax 2 + bx + c = 0 where a, b and c are numbers and x is the unknown whose value(s) we wish to find.
More informationA. a change in demand. B. a change in quantity demanded. C. a change in quantity supplied. D. unit elasticity. E. a change in average variable cost.
1. The supply of gasoline changes, causing the price of gasoline to change. The resulting movement from one point to another along the demand curve for gasoline is called A. a change in demand. B. a change
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Chapter 11 Monopoly practice Davidson spring2007 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A monopoly industry is characterized by 1) A)
More informationProblems: Table 1: Quilt Dress Quilts Dresses Helen 50 10 1.8 9 Carolyn 90 45 1 2
Problems: Table 1: Labor Hours needed to make one Amount produced in 90 hours: Quilt Dress Quilts Dresses Helen 50 10 1.8 9 Carolyn 90 45 1 2 1. Refer to Table 1. For Carolyn, the opportunity cost of 1
More informationChapter 6: Break-Even & CVP Analysis
HOSP 1107 (Business Math) Learning Centre Chapter 6: Break-Even & CVP Analysis One of the main concerns in running a business is achieving a desired level of profitability. Cost-volume profit analysis
More informationMaximizing volume given a surface area constraint
Maximizing volume given a surface area constraint Math 8 Department of Mathematics Dartmouth College Maximizing volume given a surface area constraint p.1/9 Maximizing wih a constraint We wish to solve
More informationFINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA
FINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA 1.1 Solve linear equations and equations that lead to linear equations. a) Solve the equation: 1 (x + 5) 4 = 1 (2x 1) 2 3 b) Solve the equation: 3x
More information