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11th Edition

Ronald J. Harshbarger + 1 other

Publisher: Cengage Learning

ISBN: 9781305108042

Chapter 14.4, Problem 13E

Textbook Problem

In Problems 1-16, find each function’s relative maxima, relative minima, and saddle points, if they exist.

Mathematical Applications for the Management, Life, and Social Sciences

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Ch. 14.1 - CHECKPOINT
1. Find the domain of the function
Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - Give the domain of each function in Problems...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...

Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 9-14, evaluate the functions at the...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - 23. Investment The future value S of an investment...Ch. 14.1 - 24. Amortization If $100,000 is borrowed to...Ch. 14.1 - 26. Wilsons lot size formula In economics, the...Ch. 14.1 - Temperature-humidity models There are different...Ch. 14.1 - Temperature-humidity models There are different...Ch. 14.1 - 29. Mortgage The following tables show that a...Ch. 14.1 - 30. Wind chill Wind and cold temperatures combine...Ch. 14.1 - 31. Utility Suppose that the utility function for...Ch. 14.1 - 32. Utility Suppose that an indifference curve for...Ch. 14.1 - 33. Production Suppose that a company’s production...Ch. 14.1 - 34. Production Suppose that a company’s production...Ch. 14.1 - 35. Production Suppose that the number of units of...Ch. 14.1 - 36. Profit The Kirk Kelly Kandy Company makes two...Ch. 14.1 - 37. Epidemic The cost per day to society of an...Ch. 14.1 - 38. Pesticide An area of land is to be sprayed...Ch. 14.2 - CHECKPOINT
1. If , find the following.
(a)
(b)
Ch. 14.2 - CHECKPOINT
2. If , find the following.
Ch. 14.2 - CHECKPOINT
3.
(a) (b) (c) (d)
Ch. 14.2 - CHECKPOINT
4. ,find the following.
(a) zxx (b) zyy...Ch. 14.2 - CHECKPOINT
.
Ch. 14.2 -
Ch. 14.2 -
2. If
Ch. 14.2 -
3. If , find and .
Ch. 14.2 -
4. If , find and
Ch. 14.2 -
5. If
Ch. 14.2 -
6. If
Ch. 14.2 -
7. If find and .
Ch. 14.2 - 8. If find and .
Ch. 14.2 -
Ch. 14.2 -
Ch. 14.2 -
Ch. 14.2 -
Ch. 14.2 -
Ch. 14.2 -
Ch. 14.2 -
Ch. 14.2 -
16. If
Ch. 14.2 -
17. Find the partial derivative of
with...Ch. 14.2 -
18. Find the partial derivative of
with...Ch. 14.2 -
19. Find the slope of the tangent in the...Ch. 14.2 -
20. Find the slope of the tangent in the...Ch. 14.2 -
21. Find the slope of the tangent in the...Ch. 14.2 -
22. Find the slope of the tangent in the...Ch. 14.2 -
23. If , find the following.
(a) (b) (c)...Ch. 14.2 -
24. If , find the following.
(a) (b) (c)
Ch. 14.2 -
25. If , find the following.
(a) (b) (c)
Ch. 14.2 -
26. If , find the following.
(a) (b) (c)
Ch. 14.2 -
27. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
28. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
29. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
30. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 -
31. If , find the following.
(a) (b) (c) (d)...Ch. 14.2 - 32. If , find the following.
(a) (b) (c) (d)
Ch. 14.2 - 33. If , find the following.
Ch. 14.2 - 34. If , find the following.
Ch. 14.2 - .
Ch. 14.2 -
Ch. 14.2 -
Ch. 14.2 -
Ch. 14.2 -
Ch. 14.2 -
Ch. 14.2 - 41. .
Ch. 14.2 - .
Ch. 14.2 -
Ch. 14.2 -
Ch. 14.2 - 45. Mortgage When a homeowner has a 25-year...Ch. 14.2 - 46. Mass transportation ridership Suppose that in...Ch. 14.2 - 47. Wilson's lot size formula In economics, the...Ch. 14.2 - 48. Cost Suppose that the total cost (in dollars)...Ch. 14.2 - 49. Pesticide Suppose that the number of thousands...Ch. 14.2 - 50. Profit Suppose that the profit (in dollars)...Ch. 14.2 - 51. Utility If is the utility function for goods...Ch. 14.2 - 52. Utility If the utility function for goods X...Ch. 14.2 - 53. Production Suppose that the output Q (in...Ch. 14.2 - 54. Production Suppose that the production Q (in...Ch. 14.2 - Wind chill Dr. Paul Siple conducted studies...Ch. 14.2 - Wind chill Dr. Paul Siple conducted studies...Ch. 14.3 - CHECKPOINT
If the joint cost in dollars for two...Ch. 14.3 - CHECKPOINT
2. If the production function for a...Ch. 14.3 - CHECKPOINT
3. If the demand functions for two...Ch. 14.3 - 1. The cost (in dollars) of manufacturing one item...Ch. 14.3 - 2. The manufacture of 1 unit of a product has a...Ch. 14.3 - 3. The total cost of producing 1 unit of a product...Ch. 14.3 - 4. The total cost of producing an item is
...Ch. 14.3 - 5. The total cost of producing 1 unit of a product...Ch. 14.3 - 6. The total cost of producing 1 unit of a product...Ch. 14.3 - 7. The joint cost (in dollars) for two products is...Ch. 14.3 - 8. The joint cost (in dollars) for products X and...Ch. 14.3 - 9. If the joint cost function for two products is
...Ch. 14.3 - 10. Suppose the joint cost function for x units of...Ch. 14.3 - 11. Suppose that the joint cost function for two...Ch. 14.3 - 12. Suppose that the joint cost function for two...Ch. 14.3 - 13. Suppose that the production function for a...Ch. 14.3 - 14. Suppose the production function for a product...Ch. 14.3 - 15. Suppose that the production function for a...Ch. 14.3 - 16. Suppose that a company’s production function...Ch. 14.3 - For Problems 17-19, suppose that the number of...Ch. 14.3 - For Problems 17-19, suppose that the number of...Ch. 14.3 - For Problems 17-19, suppose that the number of...Ch. 14.3 - 20. If a production function is given by , find...Ch. 14.3 - 21. Suppose the Cobb-Douglas production function...Ch. 14.3 - 22. Suppose the Cobb-Douglas production function...Ch. 14.3 - In Problems 23-26, prices and are in dollars and...Ch. 14.3 - In Problems 23-26, prices and are in dollars and...Ch. 14.3 - In Problems 23-26, prices and are in dollars and...Ch. 14.3 - In Problems 23-26, prices and are in dollars and...Ch. 14.3 - In Problems 27-30, the demand functions for and ...Ch. 14.3 - In Problems 27-30, the demand functions for and ...Ch. 14.3 - In Problems 27-30, the demand functions for and ...Ch. 14.3 - In Problems 27-30, the demand functions for and ...Ch. 14.4 - CHECKPOINT
Suppose that
Find
Ch. 14.4 - CHECKPOINT
Suppose that
2. Solve simultaneously...Ch. 14.4 - CHECKPOINT
Suppose that .
3. Test the point(s) for...Ch. 14.4 - CHECKPOINT
4. Use linear regression to write the...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each functions relative...Ch. 14.4 - In Problems 1-16, find each functions relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 1-16, find each function’s relative...Ch. 14.4 - In Problems 17 and 18, use the points given in the...Ch. 14.4 - In Problems 17 and 18, use the points given in the...Ch. 14.4 - 19. Profit Suppose that the quarterly profit from...Ch. 14.4 - 20. Profit The profit from the sales of two...Ch. 14.4 - 21. Nutrition A new food is designed to add weight...Ch. 14.4 - 22. Profit The profit for a grain crop is related...Ch. 14.4 - 23. Production Suppose that
tons
is the...Ch. 14.4 - 24. Production Suppose that x units of one input...Ch. 14.4 - 25. Profit Suppose that a manufacturer produces...Ch. 14.4 - 26. Profit Suppose that a firm produces two...Ch. 14.4 - 27. Manufacturing Find the values for each of the...Ch. 14.4 - 28. Manufacturing Find the values for each of the...Ch. 14.4 - 29. Profit A company manufactures two products, A...Ch. 14.4 - 30. Production Let x be the number of work-hours...Ch. 14.4 - The manager of the Sea Islands Chicken Shack is...Ch. 14.4 - The manager of the Sea Islands Chicken Shack is...Ch. 14.4 - Retirement benefits The table gives the...Ch. 14.4 - World population The table gives the actual or...Ch. 14.4 - Student loans The following table shows the...Ch. 14.5 - CHECKPOINT
Find the minimum value of
1. forming...Ch. 14.5 - CHECKPOINT
Find the minimum value of , subject to...Ch. 14.5 - CHECKPOINT
Find the minimum value of
3. setting...Ch. 14.5 - CHECKPOINT
Find the minimum value of
4. finding...Ch. 14.5 - 1. Find the minimum value of subject to the...Ch. 14.5 - 2. Find the maximum value of subject to .
Ch. 14.5 - 3. Find the minimum value of subject to the...Ch. 14.5 - 4. Find the maximum value of subject to the...Ch. 14.5 - 5. Find the maximum value of subject to .
Ch. 14.5 - 6. Find the maximum value of the function subject...Ch. 14.5 - 7. Find the maximum value of the function subject...Ch. 14.5 - 8. Find the minimum value of subject to the...Ch. 14.5 - 9. Find the maximum value of subject to .
Ch. 14.5 - 10. Find the maximum value of subject to .
Ch. 14.5 - 11. Find the minimum value of subject to the...Ch. 14.5 - 12. Find the minimum value of subject to the...Ch. 14.5 - 13. Find the maximum value of subject to the...Ch. 14.5 - 14. Find the maximum value of subject to the...Ch. 14.5 - 5. Utility Suppose that the utility function for...Ch. 14.5 - 16. Utility Suppose that the budget constraint in...Ch. 14.5 - 17. Utility Suppose that the utility function for...Ch. 14.5 - 18. Utility Suppose that the utility function for...Ch. 14.5 - 19. Production Suppose a company has the...Ch. 14.5 - 20. Production Suppose a company has the...Ch. 14.5 - 21. Cost A firm has two plants, X and Y. Suppose...Ch. 14.5 - 22. Cost Suppose that the cost of producing x...Ch. 14.5 - 23. Revenue On the basis of past experience, a...Ch. 14.5 - 24. Manufacturing Find the dimensions x, y, and z...Ch. 14.5 - 25. Manufacturing Find the dimensions (in...Ch. 14.5 - 26. Manufacturing Show that a box with a square...Ch. 14 - 1. What is the domain of ?
Ch. 14 - 2. What is the domain of ?
Ch. 14 - 3. If .
Ch. 14 - 4. If .
Ch. 14 - 5. Find .
Ch. 14 - 6. Find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - In Problems 7-12, find .
Ch. 14 - 13. Find the partial derivative of with respect...Ch. 14 - 14. Find the slope of the tangent in the...Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - In Problems 15-18, find the second partials.
Ch. 14 - Test z=16x2xyy2+24y for maxima and minima.Ch. 14 - Test z=x3+y312x27y for maxima and minima.Ch. 14 - 21. Find the maximum value of subject to the...Ch. 14 - 22. Find the maximum value of subject to the...Ch. 14 - 23. Utility Suppose that the utility function for...Ch. 14 - 24. Savings plans The accumulated value A of a...Ch. 14 - 25. Retirement benefits The monthly benefit B (in...Ch. 14 - 26. Advertising and sales The number of units of...Ch. 14 - 27. Cost The joint cost, in dollars, for two...Ch. 14 - 28. Production Suppose that the production...Ch. 14 - 29. Marginal demand The demand functions for...Ch. 14 - 30. Marginal demand Suppose that the demand...Ch. 14 - 31. Profit The weekly profit (in dollars) from the...Ch. 14 - 32. Cost Suppose a company has two separate plants...Ch. 14 - 33. Utility If the utility function for two...Ch. 14 - 34. Production Suppose a company has the...Ch. 14 - 35. Modeling US. average wage The table gives the...Ch. 14 - 36. Modeling Civilian workforce The following...Ch. 14 - 1. Consider the function .
(a) Find the domain of...Ch. 14 - 2. Find all first and second partial derivatives...Ch. 14 - 3. Let . Find the pairs that are critical points...Ch. 14 - 4. Suppose a company’s monthly production value Q...Ch. 14 - 5. The monthly payment R on a loan is a function...Ch. 14 - 6. Let . Find .
Ch. 14 - 7. Suppose the demand functions for two products...Ch. 14 - 8. Suppose a store sells two brands of disposable...Ch. 14 - 9. Find x and y that maximize the utility function...Ch. 14 - In the last half of the twentieth century the U.S....

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