Calculus and Its Applications (11th Edition)
11th Edition
ISBN: 9780321979391
Author: Marvin L. Bittinger, David J. Ellenbogen, Scott J. Surgent
Publisher: PEARSON
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Textbook Question
Chapter 6.5, Problem 45E
Discuss the difference between solving maximum-minimum problem using the method of Lagrange multipliers and the method of Section 6.3
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Chapter 6 Solutions
Calculus and Its Applications (11th Edition)
Ch. 6.1 - Forf(x,y)=x23xy,find(0,2),f(2,3),andf(10,5).Ch. 6.1 - 2. .
Ch. 6.1 - 3. .
Ch. 6.1 - 4. .
Ch. 6.1 - Forf(x,y)=Inx+y3,findf(e,2),f(e2,4),andf(e3,5).Ch. 6.1 - 6. .
Ch. 6.1 - Forf(x,y,z)=x2y2+z2,findf(1,2,3)andf(2,1,3).Ch. 6.1 - 8. .
Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...
Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - 15. Price-earnings ratio. The price-earnings ratio...Ch. 6.1 - Yield. The yield of a stock is given by Y(D,P)=DP,...Ch. 6.1 - 17. Cost of storage equipment. Consider the cost...Ch. 6.1 - Savings and interest. A sum of $1000 is deposited...Ch. 6.1 - Monthly car payments. Ashley wants to buy a 2014...Ch. 6.1 - Prob. 20ECh. 6.1 - 21. Poiseuille’s Law. The speed of blood in a...Ch. 6.1 - Prob. 22ECh. 6.1 - 23. Body surface area. The Mosteller formula for...Ch. 6.1 - Body surface area. The Haycock formula for...Ch. 6.1 - 25. Goals against average. A hockey goalie’s goals...Ch. 6.1 - 26. Dewpoint. The dewpoint is the temperature at...Ch. 6.1 - For the tornado described in Exercise 22, if the...Ch. 6.1 - According to the Mosteller formula in Exercise 23,...Ch. 6.1 - Explain the difference between a function of two...Ch. 6.1 - 30. Find some examples of function of several...Ch. 6.1 - Wind Chill Temperature. Because wind speed...Ch. 6.1 - Wind Chill Temperature.
Because wind speed...Ch. 6.1 - Prob. 33ECh. 6.1 - Wind Chill Temperature.
Because wind speed...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.1 - Prob. 40ECh. 6.1 - Use a 3D graphics program to generate the graph of...Ch. 6.2 - Find zx,zy,zx|(2,3),andzy|(0,5) z=7x5yCh. 6.2 - Find zx,zy,zx|(2,3),andzy|(0,5) z=2z3yCh. 6.2 - Prob. 3ECh. 6.2 - Find zx,zy,zx|(2,3),andzy|(0,5) z=2x3+3xyxCh. 6.2 - .
5.
Ch. 6.2 - .
6.
Ch. 6.2 - Find.
7.
Ch. 6.2 - Find fx,fy,fz(2,1),andfy(3,2). f(x,y)=x2y2Ch. 6.2 - Find
9.
Ch. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Find fxandfy f(x,y)=xy+y5xCh. 6.2 - Prob. 19ECh. 6.2 - Find
20.
Ch. 6.2 - Find fbandfm f(b,m)=m3+4m2bb2+(2m+b5)2+(3m+b6)2Ch. 6.2 - Find fbandfm f(b,m)=5m2mb23b+(2m+b8)2+(3m+b9)2Ch. 6.2 - Find fx,fy,andf (The symbol is the Greek letter...Ch. 6.2 - Find (The symbol is the Greek letter...Ch. 6.2 - Find fx,fy,andf (The symbol is the Greek letter...Ch. 6.2 - Find fx,fy,andf (The symbol is the Greek letter...Ch. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Find the four second-order partial derivatives....Ch. 6.2 - Find the four second-order partial derivatives....Ch. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Find fxy,fxy,fyx,andfyy. (Remember, fyx means to...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find. (Remember, means to differentiate with...Ch. 6.2 - Find fxy,fxy,fyx,andfyy. (Remember, fyx means to...Ch. 6.2 - The Cobb-Douglas model. Riverside Appliances has...Ch. 6.2 - The Cobb-Douglas model. Lincolnville Sporting...Ch. 6.2 - A study of Texas nursing homes found that the...Ch. 6.2 - A study of Texas nursing homes found that the...Ch. 6.2 - Prob. 45ECh. 6.2 - Temperaturehumidity Heat Index. In summer, higher...Ch. 6.2 - Temperaturehumidity Heat Index. In summer, higher...Ch. 6.2 - Prob. 48ECh. 6.2 - Use the equation for Th given above for Exercises...Ch. 6.2 - Use the equation for Th given above for Exercises...Ch. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Reading Ease
The following formula is used by...Ch. 6.2 - Reading Ease
The following formula is used by...Ch. 6.2 - Prob. 55ECh. 6.2 - Reading Ease The following formula is used by...Ch. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Find fxandft. f(x,t)=(x2+t2x2t2)5Ch. 6.2 - In Exercises 63 and 64, find fxx,fxy,fyx,andfyy...Ch. 6.2 - In Exercises 63 and 64, find fxx,fxy,fyx,andfyy...Ch. 6.2 - Do some research on the Cobb-Douglas production...Ch. 6.2 - Prob. 66ECh. 6.2 - Considerf(x,y)=In(x2+y2). Show that f is a...Ch. 6.2 - Consider f(x,t)=x35xy2 Show that f is a solution...Ch. 6.2 - Prob. 69ECh. 6.3 - Find the relative maximum and minimum values. ...Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values. ...Ch. 6.3 - Find the relative maximum and minimum values....Ch. 6.3 - Find the relative maximum and minimum values. ...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 15-22, assume that relative maximum...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - In Exercises 23-26, find the relative maximum and...Ch. 6.3 - Is a cross-section of an anticlastic curve always...Ch. 6.3 - Explain the difference between a relative minimum...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.3 - Use a 3D graphics program to graph each of the...Ch. 6.4 - In Exercises 1 4, find the regression line for...Ch. 6.4 - In Exercises 1 – 4, find the regression line for...Ch. 6.4 - In Exercises 1 4, find the regression line for...Ch. 6.4 - In Exercises 1 – 4, find the regression line for...Ch. 6.4 - In Exercises 5-8, find an exponential regression...Ch. 6.4 - In Exercises 5-8, find an exponential regression...Ch. 6.4 - Prob. 7ECh. 6.4 - In Exercises 5-8, find an exponential regression...Ch. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - All of the following exercises can be done with a...Ch. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of subject to given constraint,...Ch. 6.5 - Find the extremum of f(x,y) subject to given...Ch. 6.5 - Find the extremum of subject to given constraint,...Ch. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - Prob. 13ECh. 6.5 - Prob. 14ECh. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Prob. 18ECh. 6.5 - 19. Maximizing typing area. A standard piece of...Ch. 6.5 - 20. Maximizing room area. A carpenter is building...Ch. 6.5 - 21. Minimizing surface area. An oil drum of...Ch. 6.5 - Juice-can problem. A large juice can has a volume...Ch. 6.5 - Maximizing total sales. Total sales, S, of...Ch. 6.5 - Maximizing total sales. Total sales, S, of Sea...Ch. 6.5 - 25. Minimizing construction costs. Denney...Ch. 6.5 - Minimizing the costs of container construction....Ch. 6.5 - Minimizing total cost. Each unit of a product can...Ch. 6.5 - 28. Minimizing distance and cost. A highway passes...Ch. 6.5 - 29. Minimizing distance and cost. From the center...Ch. 6.5 -
In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - In Exercises 30-33, find the absolute maximum and...Ch. 6.5 - Business: minimizing costs with constraints....Ch. 6.5 - Business: maximizing profits with constraints. A...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Find the indicated maximum or minimum value of...Ch. 6.5 - Economics: the Law of Equimarginal Productivity....Ch. 6.5 - 44. Business: maximizing production. A computer...Ch. 6.5 - 45. Discuss the difference between solving...Ch. 6.5 - Write a brief report on the life and work of the...Ch. 6.5 - Prob. 47ECh. 6.6 - Prob. 1ECh. 6.6 - Prob. 2ECh. 6.6 - Prob. 3ECh. 6.6 - Prob. 4ECh. 6.6 - Evaluate. 4113(x+5y)dxdyCh. 6.6 - Prob. 6ECh. 6.6 - Prob. 7ECh. 6.6 - Evaluate.
8.
Ch. 6.6 - Evaluate. 01x2x(x+y)dydxCh. 6.6 - Prob. 10ECh. 6.6 - Prob. 11ECh. 6.6 - Evaluate.
12.
Ch. 6.6 - Evaluate. 020x(x+y2)dydxCh. 6.6 - Prob. 14ECh. 6.6 - Find the volume of the solid capped by the surface...Ch. 6.6 - 16. Find the volume of the solid capped by the...Ch. 6.6 - 17. Find the average value of.
Ch. 6.6 - 18. Find the average value of.
Ch. 6.6 - 19. Find the average value of, where the region of...Ch. 6.6 - Prob. 20ECh. 6.6 - 21. Life sciences: population. The population...Ch. 6.6 - 22. Life sciences: population. The population...Ch. 6.6 - Prob. 23ECh. 6.6 - Prob. 24ECh. 6.6 - Prob. 25ECh. 6.6 - Is evaluated in much the same way as a double...Ch. 6.6 - 27. Describe the geometric meaning of the double...Ch. 6.6 - 28. Explain how Exercise 1 can be answered without...Ch. 6.6 - Prob. 29ECh. 6.6 - Prob. 30ECh. 6.6 - Use a calculator that does multiple integration to...Ch. 6 - Match each expression in column A with an...Ch. 6 - Given f(x,y)=ey+3xy3+2y, find each of the...Ch. 6 - Given, find each of the following
10.
Ch. 6 - Given f(x,y)=ey+3xy3+2y, find each of the...Ch. 6 - Given, find each of the following
12.
Ch. 6 - Given, find each of the following
13.
Ch. 6 - Given f(x,y)=ey+3xy3+2y, find each of the...Ch. 6 - Given, find each of the following
15.
Ch. 6 - 16. State the domain of
Ch. 6 - Given, find each of the following
17.
Ch. 6 - Given z=2x3Iny+xy2, find each of the following...Ch. 6 - Given, find each of the following
19.
Ch. 6 - Given, find each of the following
20.
Ch. 6 - Given, find each of the following
21.
Ch. 6 - Given, find each of the following
22.
Ch. 6 - Find the relative maximum and minimum values [6.3]...Ch. 6 - Find the relative maximum and minimum values [6.3]...Ch. 6 - Find the relative maximum and minimum values [6.3]...Ch. 6 - Prob. 26RECh. 6 - 27. Consider the data in the following table...Ch. 6 - Consider the data in the table below regarding...Ch. 6 - 29. Find the extremum of Minimum
subject...Ch. 6 - Find the extremum of f(x,y)=6xy subject to the...Ch. 6 - Find the absolute maximum and minimum values of...Ch. 6 - Evaluate [6.6] 0112x2y3dydxCh. 6 - Evaluate
[6.6]
33.
Ch. 6 - Business: demographics. The density of students...Ch. 6 - 35. Evaluate
.
Ch. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Given, find each of the following
1.
Ch. 6 - Prob. 2TCh. 6 - Given f(x,y)=ex+2x3y+y, find each of the following...Ch. 6 - Prob. 4TCh. 6 - Given, find each of the following
5.
Ch. 6 - Given, find each of the following
6.
Ch. 6 - Given f(x,y)=ex+2x3y+y, find each of the following...Ch. 6 - Find the relative maximum and minimum values....Ch. 6 - Prob. 9TCh. 6 - Prob. 10TCh. 6 - Prob. 11TCh. 6 - Prob. 12TCh. 6 - Prob. 13TCh. 6 - 14. Business: maximizing production. Southwest...Ch. 6 - Find fxandft: f(x,t)=x22tx3+2t.Ch. 6 - Use a 3D graphics program to graph...
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- 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.arrow_forwardCan you help with this question?arrow_forwardUse Lagrange multipliers to find the maximum volume of a box inside a sphere of radius 12cm. -Make a diagram that illustrates the problem statement -shows and explains the equation to maximize and the restriction equation -develop the lagrange multipliers and solve the system -displays the result of the variables and defines the maximum volumearrow_forward
- Maximize the total output f = X1 + X2 + X3 (production from three distinct processes) subject to input constraints (limitation of time available for production) 5.x1 + 6x2 + 7x3 = 12, 7x1 + 4x2 + x3 = 12.arrow_forwardFollow the steps in the diagram "Simplex Method Summarized" in Section 6-2 in the textbook to maximize z = 2x, + 3x, + 2x,, subject to the system 2x, + х, + 2х, S 13 X, + x, - 3x, < 8 x 2 0, x, 2 0, x, 2 0arrow_forward3. (Section 15.8) A rectangular box (without a top) is to be constructed having a volume of 54 in³ using two different materials. The material for the bottom is four times as costly (per square inch) as the rest of the material. Determine the dimensions of the box that will minimize the cost of materials using Lagrange multipliers.arrow_forward
- This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, у) = 4x + 8y, x² + y2 = 20 maximum value minimum valuearrow_forwardYou solve the linear optimization problem in Question III without including the con-straint from (c) using Excel solver. You obtained the sensitivity table in Table 4. Please see attached image for the Constraints/Sensitivity Table a) Which products are exhausted | or, in other words, what constraints are binding? b) Can increasing the supply of sugar result in an increased value of the objective function? c) [What is the change in revenue if the supply of butter is increased from 15; 000g to 17; 000g? d) What is the change in revenue if the supply of eggs is decreased from 35 to 31? e) If you decrease the supply of our from 17; 000g to 5; 000g then therevenue will increase, decrease, or remain the same? (f) The constraint associated with making at least 14 croissants each daywas added. The problem was resolved and the sensitivity report obtained. Theshadow price turned out to be non-zero. What is the sign of the shadow price?Positive or negative?arrow_forwardWhat are Lagrange's multipliers? Briefly explain. In what conditions Lagrange's multiplier method can be used for holonomic constraints?arrow_forward
- This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, У) бх + бу; х2 + y? %3D 18 maximum value minimum valuearrow_forwardCurrent Attempt in Progress Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = x² + 5y subject to the constraint if such values exist. Enter the exact answers. If there is no global maximum or global minimum, enter NA in the appropriate answer area. Maximum = x² - y² = 1₁ Minimum =arrow_forwardThis extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, у) 3D 4x + 8y; х? + у2 = 20 maximum value minimum valuearrow_forward
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