Mathematical Applications for the Management, Life, and Social Sciences
11th Edition
ISBN: 9781305108042
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Textbook Question
Chapter 12.4, Problem 8E
In Problems 1-12, cost, revenue, and profit are in dollars and x is the number of units.
A certain firm’s marginal cost for a product is
(a) Find the optimal level of production.
(b) Find the profit function.
(c) Find the profit or loss at the optimal level of production.
(d) Should production be continued for the short run?
(e) Should production be continued for the long run?
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Chapter 12 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
Ch. 12.1 - 1. True or false:
(a)
(b)
Ch. 12.1 - Prob. 2CPCh. 12.1 - 1. If what is
Ch. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 7ECh. 12.1 - Evaluate the integrals in Problems 5-28. Check...
Ch. 12.1 - Prob. 9ECh. 12.1 - Prob. 10ECh. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Prob. 28ECh. 12.1 - In Problems 29-32, use algebra to rewrite the...Ch. 12.1 - In Problems 29-32, use algebra to rewrite the...Ch. 12.1 - Prob. 31ECh. 12.1 - In Problems 29-32, use algebra to rewrite the...Ch. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - In each of Problems 37-40, a family of functions...Ch. 12.1 - Prob. 38ECh. 12.1 - In each of Problems 37-40, a family of functions...Ch. 12.1 - Prob. 40ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - 43. Revenue If the marginal revenue (in dollars...Ch. 12.1 - Prob. 44ECh. 12.1 - 45. Stimulus-response Suppose that when a sense...Ch. 12.1 - Prob. 46ECh. 12.1 - 47. Pollution A factory is damping pollutants into...Ch. 12.1 - 48. Population growth The rate of growth of the...Ch. 12.1 - 49. Average cost The DeWitt Company has found that...Ch. 12.1 - 50. Oil leakage An oil tanker hits a reef and...Ch. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Prob. 53ECh. 12.1 - 54. Severe weather ice makers Hail is produced in...Ch. 12.1 - 55. U.S. population With U.S. Census Bureau data...Ch. 12.1 - 56. Consumer prices The consumer price index (CPI)...Ch. 12.2 - 1. Which of the following can be evaluated with...Ch. 12.2 - Prob. 2CPCh. 12.2 - 3. True or false: Constants can be factored...Ch. 12.2 - Prob. 4CPCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - In each of Problems 5 and 6, one of parts (a) and...Ch. 12.2 - In each of Problems 5 and 6, one of parts (a) and...Ch. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Prob. 18ECh. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - 47. Revenue Suppose that the marginal revenue for...Ch. 12.2 - Prob. 46ECh. 12.2 - 49. Physical productivity The total physical...Ch. 12.2 - 50. Production The rate of production of a new...Ch. 12.2 - 51. Data entry speed The rate of change in data...Ch. 12.2 - Prob. 50ECh. 12.2 - 53. Film attendance An excellent film with a very...Ch. 12.2 - 54. Product quality and advertising An inferior...Ch. 12.2 - 55. Demographics Because of job outsourcing, a...Ch. 12.2 - 56. Franchise growth A new fast-food firm predicts...Ch. 12.3 - 1. True or false:
(a) (b)
(c) (d)
Ch. 12.3 - Prob. 2CPCh. 12.3 - Prob. 3CPCh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Evaluate the integrals in Problems 1-32.
3.
Ch. 12.3 - Prob. 4ECh. 12.3 - Evaluate the integrals in Problems 1-32.
Ch. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Evaluate the integrals in Problems 1-32.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
9.
Ch. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Evaluate the integrals in Problems 1-32.
21.
Ch. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - Prob. 28ECh. 12.3 - Evaluate the integrals in Problems 1-32.
29.
Ch. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - In Problems 37-40, a family of functions is given...Ch. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - 43. Revenue Suppose that the marginal revenue from...Ch. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - 46. Radioactive decay Radioactive substances decay...Ch. 12.3 - 47. Memorization The rate of vocabulary...Ch. 12.3 - Prob. 48ECh. 12.3 - 49. Compound interest If $P is invested for n...Ch. 12.3 - 50. Temperature changes When an object is moved...Ch. 12.3 - Prob. 56ECh. 12.4 - 1. True or false:
(a) If , then the constant of...Ch. 12.4 - Prob. 2CPCh. 12.4 - Prob. 3CPCh. 12.4 - Prob. 4CPCh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - 14. Suppose that the marginal cost for a certain...Ch. 12.4 - 14. Suppose that the marginal cost for a certain...Ch. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Suppose that the marginal propensity to save is...Ch. 12.4 - Prob. 24ECh. 12.4 - Prob. 26ECh. 12.5 - Prob. 1CPCh. 12.5 - Prob. 2CPCh. 12.5 - Prob. 3CPCh. 12.5 - Prob. 1ECh. 12.5 - Prob. 2ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - Prob. 9ECh. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - Prob. 13ECh. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Prob. 22ECh. 12.5 - Prob. 23ECh. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - Prob. 26ECh. 12.5 - Prob. 27ECh. 12.5 - Prob. 28ECh. 12.5 - Prob. 29ECh. 12.5 - Prob. 30ECh. 12.5 - In Problems 29-36, find the particular solution to...Ch. 12.5 - Prob. 32ECh. 12.5 - Prob. 33ECh. 12.5 - Prob. 34ECh. 12.5 - Prob. 35ECh. 12.5 - Prob. 36ECh. 12.5 - Prob. 37ECh. 12.5 - Prob. 38ECh. 12.5 - Prob. 39ECh. 12.5 - Prob. 40ECh. 12.5 - 41. Investing When the interest on an investment...Ch. 12.5 - Prob. 42ECh. 12.5 - 43. Bacterial growth Suppose that the growth of a...Ch. 12.5 - Prob. 44ECh. 12.5 - 46. Sales and pricing Suppose that a chain of auto...Ch. 12.5 - Prob. 46ECh. 12.5 - Prob. 47ECh. 12.5 - 48. Radioactive decay A certain radioactive...Ch. 12.5 - Prob. 49ECh. 12.5 - Prob. 50ECh. 12.5 - 51. Drug in an organ Suppose that a liquid carries...Ch. 12.5 - Prob. 52ECh. 12.5 - Prob. 53ECh. 12.5 - Prob. 54ECh. 12.5 - Prob. 55ECh. 12.5 - Prob. 56ECh. 12.5 - Prob. 57ECh. 12.5 - Prob. 58ECh. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Evaluate the integrals in Problems 1-26.
26. (a) ...Ch. 12 - Prob. 27RECh. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Prob. 34RECh. 12 - Prob. 35RECh. 12 - Prob. 36RECh. 12 - 37. Oxygen levels in water The rate of change of...Ch. 12 - Prob. 38RECh. 12 - Prob. 39RECh. 12 - Prob. 40RECh. 12 - 41. Cost The marginal cost for a product is
...Ch. 12 - Prob. 42RECh. 12 - Prob. 43RECh. 12 - Prob. 44RECh. 12 - Prob. 45RECh. 12 - Prob. 46RECh. 12 - 47. Fossil dating Radioactive beryllium is...Ch. 12 - Prob. 48RECh. 12 - Prob. 49RECh. 12 - Prob. 1TCh. 12 - Evaluate the integrals in Problems 1-11.
Ch. 12 - Prob. 3TCh. 12 - Prob. 4TCh. 12 - Prob. 5TCh. 12 - Prob. 6TCh. 12 - Prob. 7TCh. 12 - Prob. 8TCh. 12 - Prob. 9TCh. 12 - Prob. 10TCh. 12 - Prob. 11TCh. 12 - Prob. 12TCh. 12 - Prob. 13TCh. 12 - Prob. 14TCh. 12 - Prob. 15TCh. 12 - Prob. 16TCh. 12 - Prob. 17TCh. 12 - Prob. 18TCh. 12 - Prob. 19TCh. 12 - Suppose the marginal propensity to save is given...Ch. 12 - Prob. 21TCh. 12 - Prob. 22T
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