Mathematical Applications for the Management, Life, and Social Sciences
Mathematical Applications for the Management, Life, and Social Sciences
12th Edition
ISBN: 9781337625340
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 10.3, Problem 42E

A large corporation with monopolistic control in the marketplace has its average daily costs, in dollars, given by

C ¯ = 800 x 100 x + x 2

The daily demand for x units of its product is given by p =   60 , 000   −   50 x dollars. Find the quantity that gives maximum profit and find the maximum profit. What selling price should the corporation set for its product?

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Chapter 10 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 10.1 - 1. The x- values of critical points are found...Ch. 10.1 - Prob. 2CPCh. 10.1 - Prob. 3CPCh. 10.1 - Prob. 4CPCh. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - In Problems 1 and 2, use the indicated points on...Ch. 10.1 - 3. Use the graph of in Problem 1 to identify at...Ch. 10.1 - 4. Use the graph of in Problem 2 to identify at...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...Ch. 10.1 - In Problems 5 and 6, use the sign diagram for to...
Ch. 10.1 - In Problems 7-10, (a) find the critical values of...Ch. 10.1 - In Problems 7-10, (a) find the critical values of...Ch. 10.1 - In Problems 7-10, (a) find the critical values of...Ch. 10.1 - In Problems 7-10, (a) find the critical values of...Ch. 10.1 - For each function and graph in Problems 11-14 (a)...Ch. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - For each function in Problems 15-20 (a) find (b)...Ch. 10.1 - For each function in Problems 15-20 (a) find (b)...Ch. 10.1 - For each function in Problems 15-20 (a) find (b)...Ch. 10.1 - For each function in Problems 15-20 (a) find (b)...Ch. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - For each function and graph in Problems 21-24 (a)...Ch. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - For each function in Problems 25-30, find the...Ch. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - For each function in Problems 25-30, find the...Ch. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - Prob. 32ECh. 10.1 - Prob. 33ECh. 10.1 - In Problems 31-36, both a function and its...Ch. 10.1 - Prob. 35ECh. 10.1 - In Problems 31-36, both a function and its...Ch. 10.1 - Prob. 37ECh. 10.1 - Prob. 38ECh. 10.1 - Prob. 39ECh. 10.1 - Prob. 40ECh. 10.1 - Prob. 41ECh. 10.1 - Prob. 42ECh. 10.1 - Prob. 43ECh. 10.1 - Prob. 44ECh. 10.1 - Prob. 45ECh. 10.1 - In each of Problems 43-46, a graph of is given....Ch. 10.1 - Prob. 47ECh. 10.1 - Prob. 48ECh. 10.1 - 49. Advertising and sales Suppose that the daily...Ch. 10.1 - 50. Pricing and sales Suppose that a chain of auto...Ch. 10.1 - 51. Productivity A time study showed that, on...Ch. 10.1 - 52. Production Analysis of daily output of a...Ch. 10.1 - 53. Production costs Suppose that the average...Ch. 10.1 - 54. Average costs Suppose the average costs of a...Ch. 10.1 - 55. Marginal revenue Suppose the weekly marginal...Ch. 10.1 - 56. Earnings Suppose that the rate of change of...Ch. 10.1 - 57. Revenue The weekly revenue of a certain...Ch. 10.1 - 58. Medication Suppose that the concentration C of...Ch. 10.1 - Prob. 59ECh. 10.1 - 60. Medication The number of milligrams x of a...Ch. 10.1 - 61. Worldwide cell phone subscriberships In 2013,...Ch. 10.1 - 62. Economic dependency ratio The economic...Ch. 10.1 - Prob. 63ECh. 10.1 - 64. Modeling Energy from crude oil The table shows...Ch. 10.1 - Prob. 65ECh. 10.2 - 1. If then is concave__________. Ch. 10.2 - 2. At what value of x does the graph have a point...Ch. 10.2 - 3. On the graph below, locate any points of...Ch. 10.2 - 4. Determine whether the following is true or...Ch. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - In Problems 1-4, determine whether each function...Ch. 10.2 - In Problems 5-10, use the indicated x-values on...Ch. 10.2 - In Problems 5-10, use the indicated x-values on...Ch. 10.2 - In Problems 5-10, use the indicated x-values on...Ch. 10.2 - In Problems 5-10, use the indicated x-values on...Ch. 10.2 - In Problems 5-10, use the indicated x-values on...Ch. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - In Problems 11-14, a function and its graph are...Ch. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Find the relative maxima, relative minima, and...Ch. 10.2 - Find the relative maxima, relative minima, and...Ch. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - In Problems 29 and 30, use the graph shown in the...Ch. 10.2 - In Problems 29 and 30, use the graph shown in the...Ch. 10.2 - In Problems 31 and 32, a graph is given. Tell...Ch. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - 37. Production Suppose that the total number of...Ch. 10.2 - 38. Poiscuille's law—velocity of blood According...Ch. 10.2 - 39. Advertising and sales—diminishing returns...Ch. 10.2 - 40. Oxygen purity—diminishing returns Suppose that...Ch. 10.2 - Prob. 41ECh. 10.3 - 1. True or false: If is the total revenue...Ch. 10.3 - Prob. 2CPCh. 10.3 - Prob. 3CPCh. 10.3 - Prob. 4CPCh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - In Problems 1-6, find the absolute maxima and...Ch. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - 7. (a) If the total revenue function for a hammer...Ch. 10.3 - 8. (a) If the total revenue function for a blender...Ch. 10.3 - 9. If the total revenue function for a computer is...Ch. 10.3 - 10. A firm has total revenues given by for x...Ch. 10.3 - 11. An agency charges $100 per person for a trip...Ch. 10.3 - 12. A company handles an apartment building with...Ch. 10.3 - 13. A cable TV company has 4000 customers paying...Ch. 10.3 - 14. If club members charge $5 admission to a...Ch. 10.3 - Prob. 15ECh. 10.3 - 16. For the revenue function given by (a) find...Ch. 10.3 - 17. If the total cost function for a lamp is ...Ch. 10.3 - 18. If the total cost function for a product is ...Ch. 10.3 - 19. If the total cost function for a product is ...Ch. 10.3 - Prob. 20ECh. 10.3 - 21. If the total cost function for a product is ...Ch. 10.3 - 22. If the total cost function for a product is ...Ch. 10.3 - 23. For the cost function , show that average...Ch. 10.3 - 24. For the cost function , show that average...Ch. 10.3 - The graphs in Problems 25 and 26 show total cost...Ch. 10.3 - Prob. 26ECh. 10.3 - 27. If the profit function for a product is ...Ch. 10.3 - 28. If the profit function for a commodity is ...Ch. 10.3 - 29. A manufacturer estimates that its product can...Ch. 10.3 - 30. A product can be produced at a total cost ...Ch. 10.3 - 31. A firm can produce only 1000 units per month....Ch. 10.3 - 32. A firm can produce 100 units per week. If its...Ch. 10.3 - 33. A company handles an apartment building with...Ch. 10.3 - 34. A travel agency will plan a tour for groups of...Ch. 10.3 - 35. A firm has monthly average costs, in dollars,...Ch. 10.3 - 36. A small business has weekly average costs, in...Ch. 10.3 - 37. The weekly demand function for x units of a...Ch. 10.3 - 38. The monthly demand function for x units of a...Ch. 10.3 - 39. The monthly demand function for a product sold...Ch. 10.3 - 40. The monthly demand function for x units of a...Ch. 10.3 - 41. An industry with a monopoly on a product has...Ch. 10.3 - 42. A large corporation with monopolistic control...Ch. 10.3 - 43. Coastal Soda Sales has been granted exclusive...Ch. 10.3 - 45. Marginal revenue and marginal cost The figure...Ch. 10.3 - Prob. 46ECh. 10.3 - Prob. 49ECh. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.4 - Suppose we want to find the minimum value of and...Ch. 10.4 - Prob. 2CPCh. 10.4 - Prob. 3CPCh. 10.4 - 1. Return to sales The manufacturer of GRIPPER...Ch. 10.4 - 2. Projectiles A ball thrown into the air from a...Ch. 10.4 - 3. Profit The profit per acre from a grove of...Ch. 10.4 - 4. Reaction rates The velocity v of an...Ch. 10.4 - 5. Productivity Analysis of daily output of a...Ch. 10.4 - 6. Productivity A time study showed that, on...Ch. 10.4 - Prob. 7ECh. 10.4 - 8. Production costs Suppose that the monthly cost...Ch. 10.4 - Prob. 9ECh. 10.4 - Medication For Problems 9 and 10, consider that...Ch. 10.4 - 11. Advertising and sales An inferior product with...Ch. 10.4 - Prob. 12ECh. 10.4 - 13. News impact Suppose that the percent p (as a...Ch. 10.4 - 14. Candidate recognition Suppose that in an...Ch. 10.4 - 15. Minimum fence Two equal rectangular lots are...Ch. 10.4 - 16. Minimum fence The running yard for a dog...Ch. 10.4 - 17. Minimum cost A rectangular field with one side...Ch. 10.4 - 18. Minimum cost From a tract of land, a developer...Ch. 10.4 - 19. Optimization at a fixed cost A rectangular...Ch. 10.4 - 20. Minimum cost A 4-pen kennel of 640 square feet...Ch. 10.4 - 21. Minimum cost The base of a rectangular box is...Ch. 10.4 - Prob. 22ECh. 10.4 - 23. Inventory cost model Suppose that a company...Ch. 10.4 - 24. Inventory cost model Suppose that a company...Ch. 10.4 - 25. Inventory cost model A company needs 150,000...Ch. 10.4 - Prob. 26ECh. 10.4 - 27. Volume A rectangular box with a square base is...Ch. 10.4 - Prob. 28ECh. 10.4 - 29. Revenue The owner of an orange grove must...Ch. 10.4 - 30. Minimum material (a) A box with an open top...Ch. 10.4 - 31. Minimum cost A printer has a contract to print...Ch. 10.4 - 32. Shortest time A vacationer on an island 8...Ch. 10.4 - Prob. 33ECh. 10.5 - Prob. 1CPCh. 10.5 - Prob. 2CPCh. 10.5 - In Problems 1-4, a function and its graph are...Ch. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - Prob. 9ECh. 10.5 - Prob. 10ECh. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Prob. 13ECh. 10.5 - Prob. 14ECh. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - In Problems 19-24, a function and its first and...Ch. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - For each function in Problems 29-34, complete the...Ch. 10.5 - Prob. 33ECh. 10.5 - Prob. 34ECh. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - 37. Revenue A recently released film has its...Ch. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - 40. Profit An entrepreneur starts new companies...Ch. 10.5 - 41. Productivity The figure is a typical graph of...Ch. 10.5 - Prob. 42ECh. 10.5 - 43. Females in the workforce For selected years...Ch. 10 - In Problems 1-4, find all critical points and...Ch. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Prob. 26RECh. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Prob. 35RECh. 10 - Prob. 36RECh. 10 - Prob. 37RECh. 10 - 38. Productivity—diminishing returns Suppose the...Ch. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Prob. 41RECh. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - 45. Reaction to a drug The reaction R to an...Ch. 10 - Prob. 46RECh. 10 - 47. Population Population estimates show that the...Ch. 10 - Prob. 48RECh. 10 - 49. Product design A playpen manufacturer wants to...Ch. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - Prob. 52RECh. 10 - 53. Inventory cost model A company needs to...Ch. 10 - Prob. 54RECh. 10 - Prob. 55RECh. 10 - Prob. 1TCh. 10 - Prob. 2TCh. 10 - Prob. 3TCh. 10 - Prob. 4TCh. 10 - Prob. 5TCh. 10 - Prob. 6TCh. 10 - Prob. 7TCh. 10 - Prob. 8TCh. 10 - 9. Use the following graph of y = f(x) and the...Ch. 10 - Prob. 10TCh. 10 - Prob. 11TCh. 10 - Prob. 12TCh. 10 - 13. The revenue function for a product is dollars...Ch. 10 - Prob. 14TCh. 10 - 15. A firm sells 100 TVs per month at $300 each,...Ch. 10 - 16. An open-top box is made by cutting squares...Ch. 10 - Prob. 17T
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