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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 7.6, Problem 45E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 3CP
Problem 4CP
Problem 1SWU
Problem 2SWU
Problem 3SWU
Problem 4SWU
Problem 5SWU
Problem 6SWU
Problem 7SWU
Problem 8SWU
Problem 9SWU
Problem 10SWU
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Advertising A private golf club is determining how to spend its $8100 advertising budget. The club knows from prior experience that the number of responses A is given by

A =   0.0001 t 2 p r 1.5 where t is the number of cable television ads, p is the number of newspaper ads. and r is the number of radio ads. A cable television ad costs $90, a newspaper ad costs $36, and a radio ad costs $45.

(a) How much should be spent on each type of advertising to obtain the maximum number of responses? (Assume the golf club uses each type of advertising.)

(b) What is the maximum number of responses expected?

(a)

To determine

To calculate: The amount that should be spent on each type of advertising to obtain the maximum number of response.

Explanation

Given Information:

A private golf club is determining how to spend its $8100 advertising budget. The club knows from prior experience that the number of response A=0.0001t2pr1.5. t is the cable television ads cost $90, p is the numer of newspaper ads cost $36, r is the number of radio ads cost $45.

Formula used:

Method of Lagrange multipliers,

If the function f(x,y) contains a maximum or minimum subject to the constraint g(x,y)=0

Then the maximum or minimum can occur at one of the critical numbers of the function F is,

F(x,y,λ)=f(x,y)−λg(x,y) where, λ is a Lagrange multiplier.

Steps to determine the minimum or maximum of the function f.

1. Solve the system of equations,

Fx(x,y,λ)=0Fy(x,y,λ)=0 Fλ(x,y,λ)=0

2. Determine the value of the function f at each solution obtained from the step 1.

The largest value gives the maximum value of function f subject to the constraint g(x,y)=0 and the lowest value gives the minimum value of function f subject to the constraint g(x,y)=0.

Calculation:

Consider the function,

A=0.0001t2pr1.5 Subject to constraint 90t+36p+45r=8100

Maximize A=0.0001t2pr1.5 subject to constraint 90t+36p+45r=8100

F(A)=0.0001t2pr1.5−λ(90t+36p+45r−8100)

Thus,

Ft=0.0002t2pr1.5−90λFp=0.0001t2pr1.5−36λF=r0.00015t2pr1

(b)

To determine

To calculate: The maximum number of response exceeds.

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Sect-7.1 P-1CPSect-7.1 P-2CPSect-7.1 P-3CPSect-7.1 P-4CPSect-7.1 P-5CPSect-7.1 P-6CPSect-7.1 P-7CPSect-7.1 P-1SWUSect-7.1 P-2SWUSect-7.1 P-3SWU
Sect-7.1 P-4SWUSect-7.1 P-5SWUSect-7.1 P-6SWUSect-7.1 P-7SWUSect-7.1 P-8SWUSect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10ESect-7.1 P-11ESect-7.1 P-12ESect-7.1 P-13ESect-7.1 P-14ESect-7.1 P-15ESect-7.1 P-16ESect-7.1 P-17ESect-7.1 P-18ESect-7.1 P-19ESect-7.1 P-20ESect-7.1 P-21ESect-7.1 P-22ESect-7.1 P-23ESect-7.1 P-24ESect-7.1 P-25ESect-7.1 P-26ESect-7.1 P-27ESect-7.1 P-28ESect-7.1 P-29ESect-7.1 P-30ESect-7.1 P-31ESect-7.1 P-32ESect-7.1 P-33ESect-7.1 P-34ESect-7.1 P-35ESect-7.1 P-36ESect-7.1 P-37ESect-7.1 P-38ESect-7.1 P-39ESect-7.1 P-40ESect-7.1 P-41ESect-7.1 P-42ESect-7.1 P-43ESect-7.1 P-44ESect-7.2 P-1CPSect-7.2 P-2CPSect-7.2 P-3CPSect-7.2 P-1SWUSect-7.2 P-2SWUSect-7.2 P-3SWUSect-7.2 P-4SWUSect-7.2 P-5SWUSect-7.2 P-6SWUSect-7.2 P-1ESect-7.2 P-2ESect-7.2 P-3ESect-7.2 P-4ESect-7.2 P-5ESect-7.2 P-6ESect-7.2 P-7ESect-7.2 P-8ESect-7.2 P-9ESect-7.2 P-10ESect-7.2 P-11ESect-7.2 P-12ESect-7.2 P-13ESect-7.2 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Calculus (MindTap Course List)

Construct a frequency distribution table for the following set of scores. Include columns for proportion and pe...

Statistics for The Behavioral Sciences (MindTap Course List)

Statistical Literacy What symbol is used for the arithmetic mean when it is a sample statistic? What symbol is ...

Understanding Basic Statistics

Trees grow faster and form wider rings in warm years and grow more slowly and form narrower rings in cooler yea...

Single Variable Calculus

In problems 45-48, determine a value for that makes each statement true. 47.

Mathematical Applications for the Management, Life, and Social Sciences

Convert the expressions in Exercises 8596 radical form. 32x1/4

Finite Mathematics

For Problems 1-14, state the property that justifies each of the statements. For example, 3+(4)=(4)+3 because o...

Intermediate Algebra

Verify that the following set is an infinite set by illustrating a one-to-one correspondence between the elemen...

Mathematical Excursions (MindTap Course List)

An electronics store is offering a special price on a complete set of components (receiver, compact disc player...

Probability and Statistics for Engineering and the Sciences

Find the limit. Use lHospitals Rule where appropriate. If there is a more elementary method, consider using it....

Single Variable Calculus: Early Transcendentals

Use the following financial information to prepare an income statement for Cutting Edge Manufacturing. Inc., fo...

Contemporary Mathematics for Business & Consumers

Simplify: 912

Elementary Technical Mathematics

Perform the following operation. Reduce if possible. 1x1y

Trigonometry (MindTap Course List)

Given that ab and c0, which is correct acbc or acbc?

Elementary Geometry For College Students, 7e

15. Prove that if for all in the group , then is abelian.

Elements Of Modern Algebra

Determine all real numbers a0 for which there exists a nonnegative alive continuous function f(x) defined on 0,...

Calculus of a Single Variable

True or False? In Exercises 97-100, determine whether the statement is true or false. If it is false, explain w...

Calculus: Early Transcendental Functions (MindTap Course List)

A rectangle has dimensions of 6 in. by 3 in. Find the exact volume of the solid of revolution formed when the r...

Elementary Geometry for College Students

MARKET EQUILIBRIUM FOR REFRIGERATORS The demand equation for the Cold Spot compact refrigerator is 2x+7p1760=0,...

Finite Mathematics for the Managerial, Life, and Social Sciences

sec1(23)= a) 3 b) 3 c) 6 d) 6

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Revenue In Exercises 17 and 18, two models R1 and R2 are given for revenue (in millions of dollars) for a corpo...

Calculus (MindTap Course List)

Approximating Solution Points Using Technology In Exercises 17 and 18, use a graphing utility to graph the equa...

Calculus

Verifying that a Series Converges In Exercises 21-24, use the power series solution of the differential equatio...

Multivariable Calculus

Let F(x, y, z) = zi − xj + yk, let C be the circle x2 + y2 = 36, z = 0, and let S be the surface given by z = 3...

Study Guide for Stewart's Multivariable Calculus, 8th

Describe the disadvantages of a multiple-treatment design, compared to a two-treatment design, for a within-sub...

Research Methods for the Behavioral Sciences (MindTap Course List)

A drug store chain has stores in four cities: 38 stores in Indianapolis. 45 in Louisville, 80 in St. Louis, and...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Solve each of the following equations using the subtraction principle of equality. Check each answer. 51=48+E

Mathematics For Machine Technology

Show that a+b+c+d2=a2+b2+c2+d2+2ab+2ac+2ad+2bc+2bd+2cd.

College Algebra (MindTap Course List)

Fire ants can have a negative impact on other ant species. To investigate whether the use of bait traps is effe...

Introduction To Statistics And Data Analysis

In addition to the key words, you should also be able to define each of the following terms: Descriptive resear...

Research Methods for the Behavioral Sciences (MindTap Course List)

Consider the following set of rankings for a sample of 10 elements. a. Compute the Spearman rank-correlation co...

Statistics for Business & Economics, Revised (MindTap Course List)

In Exercises 7-12, answer the questions for the spherical model of Riemannian geometry. What is the minimum num...

Mathematics: A Practical Odyssey

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