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

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Chapter 7.9, Problem 31E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Problem 1E
Problem 2E
Problem 3E
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Problem 5E
Problem 6E
Problem 7E
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Problem 22E
Problem 23E
Problem 24E
Problem 25E
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Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Average Weekly Profit A firm’s weekly profit P (in dollars) in marketing two products is given by

P = 192 x 1 + 576 x 2 − x 1 2 − 5 x 2 2 − 2 x 1 x 2 − 5000 where x1 and x2 represent the numbers of units of each product sold weekly. Estimate the average weekly profit when x1 varies between 40 and 50 units and x2 varies between 45 and 50 units.

To determine

To calculate: The average weekly profit P (in dollars) in marketing two product is given by P=192x1+576x2−x12−x22−2x1x2−5000 when x1 varies between 40 units and 50 units and x2 varies between 45 units and 50 units.

Explanation

Given information:

The average weekly profit P (in dollars) in marketing two product is given by P=192x1+576x2−x12−x22−2x1x2−5000.

Where x1 and x2 represent the number of units of each product sold weekly.

Formula used:

The average value of integrable function z=f(x,y) over the region R with area A is;

Average value=1A∬Rf(x,y)dxdy

Calculation:

Consider equation of function,

P=192x1+576x2−x12−x22−2x1x2−5000

Here x1 varies between 40 units and 50 units and x2 varies between 45 units and 50 units.

The area of region is 50 units.

Now apply, the formula of the average value of integrable function P=192x1+576x2−x12−x22−2x1x2−5000 with x1 varies between 40 units and 50 units and x2 varies between 45 units and 50 units with area 50 units is

Average value=150∫4550∫4050(192x1+576x2−x12−x22−2x1x2−5000)dx1dx2=150∫4550[96x12+576x2x1−x133−5x1x22−x

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Chapter 7.9,
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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 P-14ESect-7.2 P-15ESect-7.2 P-16ESect-7.2 P-17ESect-7.2 P-18ESect-7.2 P-19ESect-7.2 P-20ESect-7.2 P-21ESect-7.2 P-22ESect-7.2 P-23ESect-7.2 P-24ESect-7.2 P-25ESect-7.2 P-26ESect-7.2 P-27ESect-7.2 P-28ESect-7.2 P-35ESect-7.2 P-36ESect-7.2 P-37ESect-7.2 P-38ESect-7.2 P-39ESect-7.2 P-40ESect-7.2 P-41ESect-7.2 P-42ESect-7.2 P-43ESect-7.2 P-44ESect-7.2 P-45ESect-7.2 P-46ESect-7.2 P-47ESect-7.2 P-48ESect-7.2 P-49ESect-7.2 P-50ESect-7.2 P-51ESect-7.3 P-1CPSect-7.3 P-2CPSect-7.3 P-3CPSect-7.3 P-4CPSect-7.3 P-5CPSect-7.3 P-1SWUSect-7.3 P-2SWUSect-7.3 P-3SWUSect-7.3 P-4SWUSect-7.3 P-5SWUSect-7.3 P-6SWUSect-7.3 P-7SWUSect-7.3 P-8SWUSect-7.3 P-9SWUSect-7.3 P-10SWUSect-7.3 P-1ESect-7.3 P-2ESect-7.3 P-3ESect-7.3 P-4ESect-7.3 P-5ESect-7.3 P-6ESect-7.3 P-7ESect-7.3 P-8ESect-7.3 P-9ESect-7.3 P-10ESect-7.3 P-11ESect-7.3 P-12ESect-7.3 P-13ESect-7.3 P-14ESect-7.3 P-15ESect-7.3 P-16ESect-7.3 P-17ESect-7.3 P-18ESect-7.3 P-19ESect-7.3 P-20ESect-7.3 P-21ESect-7.3 P-22ESect-7.3 P-23ESect-7.3 P-24ESect-7.3 P-25ESect-7.3 P-26ESect-7.3 P-27ESect-7.3 P-28ESect-7.3 P-29ESect-7.3 P-30ESect-7.3 P-31ESect-7.3 P-32ESect-7.3 P-33ESect-7.3 P-34ESect-7.3 P-35ESect-7.3 P-36ESect-7.3 P-37ESect-7.3 P-38ESect-7.3 P-39ESect-7.3 P-40ESect-7.3 P-41ESect-7.3 P-42ESect-7.3 P-43ESect-7.3 P-44ESect-7.3 P-45ESect-7.3 P-46ESect-7.3 P-47ESect-7.3 P-48ESect-7.3 P-49ESect-7.3 P-50ESect-7.3 P-51ESect-7.3 P-53ESect-7.3 P-54ESect-7.3 P-55ESect-7.4 P-1CPSect-7.4 P-2CPSect-7.4 P-3CPSect-7.4 P-4CPSect-7.4 P-5CPSect-7.4 P-6CPSect-7.4 P-7CPSect-7.4 P-1SWUSect-7.4 P-2SWUSect-7.4 P-3SWUSect-7.4 P-4SWUSect-7.4 P-5SWUSect-7.4 P-6SWUSect-7.4 P-7SWUSect-7.4 P-8SWUSect-7.4 P-9SWUSect-7.4 P-10SWUSect-7.4 P-1ESect-7.4 P-2ESect-7.4 P-3ESect-7.4 P-4ESect-7.4 P-5ESect-7.4 P-6ESect-7.4 P-7ESect-7.4 P-8ESect-7.4 P-9ESect-7.4 P-10ESect-7.4 P-11ESect-7.4 P-12ESect-7.4 P-13ESect-7.4 P-14ESect-7.4 P-15ESect-7.4 P-16ESect-7.4 P-17ESect-7.4 P-18ESect-7.4 P-19ESect-7.4 P-20ESect-7.4 P-21ESect-7.4 P-22ESect-7.4 P-23ESect-7.4 P-24ESect-7.4 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P-20QYSect-7.5 P-21QYSect-7.5 P-22QYSect-7.5 P-23QYSect-7.5 P-24QYSect-7.5 P-25QYSect-7.5 P-26QYSect-7.6 P-1CPSect-7.6 P-2CPSect-7.6 P-3CPSect-7.6 P-4CPSect-7.6 P-1SWUSect-7.6 P-2SWUSect-7.6 P-3SWUSect-7.6 P-4SWUSect-7.6 P-5SWUSect-7.6 P-6SWUSect-7.6 P-7SWUSect-7.6 P-8SWUSect-7.6 P-9SWUSect-7.6 P-10SWUSect-7.6 P-1ESect-7.6 P-2ESect-7.6 P-3ESect-7.6 P-4ESect-7.6 P-5ESect-7.6 P-6ESect-7.6 P-7ESect-7.6 P-8ESect-7.6 P-9ESect-7.6 P-10ESect-7.6 P-11ESect-7.6 P-12ESect-7.6 P-13ESect-7.6 P-14ESect-7.6 P-15ESect-7.6 P-16ESect-7.6 P-17ESect-7.6 P-18ESect-7.6 P-19ESect-7.6 P-20ESect-7.6 P-21ESect-7.6 P-22ESect-7.6 P-23ESect-7.6 P-24ESect-7.6 P-25ESect-7.6 P-26ESect-7.6 P-27ESect-7.6 P-28ESect-7.6 P-29ESect-7.6 P-30ESect-7.6 P-31ESect-7.6 P-32ESect-7.6 P-33ESect-7.6 P-34ESect-7.6 P-35ESect-7.6 P-36ESect-7.6 P-37ESect-7.6 P-38ESect-7.6 P-39ESect-7.6 P-40ESect-7.6 P-41ESect-7.6 P-42ESect-7.6 P-43ESect-7.6 P-44ESect-7.6 P-45ESect-7.7 P-1CPSect-7.7 P-2CPSect-7.7 P-3CPSect-7.7 P-1SWUSect-7.7 P-2SWUSect-7.7 P-3SWUSect-7.7 P-4SWUSect-7.7 P-5SWUSect-7.7 P-6SWUSect-7.7 P-7SWUSect-7.7 P-8SWUSect-7.7 P-1ESect-7.7 P-2ESect-7.7 P-3ESect-7.7 P-4ESect-7.7 P-5ESect-7.7 P-6ESect-7.7 P-7ESect-7.7 P-8ESect-7.7 P-9ESect-7.7 P-10ESect-7.7 P-11ESect-7.7 P-12ESect-7.7 P-13ESect-7.7 P-14ESect-7.7 P-15ESect-7.7 P-16ESect-7.7 P-17ESect-7.7 P-18ESect-7.7 P-19ESect-7.7 P-20ESect-7.7 P-21ESect-7.7 P-22ESect-7.7 P-23ESect-7.7 P-24ESect-7.7 P-25ESect-7.7 P-26ESect-7.7 P-27ESect-7.7 P-28ESect-7.7 P-29ESect-7.7 P-30ESect-7.8 P-1CPSect-7.8 P-2CPSect-7.8 P-3CPSect-7.8 P-4CPSect-7.8 P-5CPSect-7.8 P-6CPSect-7.8 P-1SWUSect-7.8 P-2SWUSect-7.8 P-3SWUSect-7.8 P-4SWUSect-7.8 P-5SWUSect-7.8 P-6SWUSect-7.8 P-7SWUSect-7.8 P-8SWUSect-7.8 P-9SWUSect-7.8 P-10SWUSect-7.8 P-11SWUSect-7.8 P-12SWUSect-7.8 P-13SWUSect-7.8 P-14SWUSect-7.8 P-15SWUSect-7.8 P-16SWUSect-7.8 P-1ESect-7.8 P-2ESect-7.8 P-3ESect-7.8 P-4ESect-7.8 P-5ESect-7.8 P-6ESect-7.8 P-7ESect-7.8 P-8ESect-7.8 P-9ESect-7.8 P-10ESect-7.8 P-11ESect-7.8 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Single Variable Calculus: Early Transcendentals

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Principal Rate (%) Time Interest ________________________________________________________________ $13,200 9.2 _...

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Writing a Vector in Different Forms In Exercises 9-16. the initial and terminal points of a vector v are given,...

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The area of the region at the right is:

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Describe the basic characteristics of a pre-post design and explain why these designs are not true experiments.

Research Methods for the Behavioral Sciences (MindTap Course List)

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An MBA new-matriculants survey provided the following data for 2018 students. a. For a randomly selected MBA st...

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

To perform a certain type of blood analysis, lab technicians must perform two procedures.The first procedure re...

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Let z denote a random variable that has a standard normal distribution. Determine each of the following probabi...

Introduction To Statistics And Data Analysis

Based on the following descriptions of studies, determine whether each of the studies can be classified as basi...

Research Methods for the Behavioral Sciences (MindTap Course List)

Self Check Milk containing 40 butterfat is mixed with 8 gallons of milk containing 1 butterfat to make a low-fa...

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