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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Chapter 10.1, Problem 42E
To determine
To calculate: The location of critical points from the derivation of the function
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9.22 Develop, debug, and test a program in either a high-level language or a macro
language of your choice to solve a system of equations with Gauss-Jordan elimination
without partial pivoting. Base the program on the pseudocode from Fig. 9.10. Test the
program using the same system as in Prob. 9.18. Compute the total number of flops in
your algorithm to verify Eq. 9.37.
FIGURE 9.10
Pseudocode to implement the
Gauss-Jordan algorithm with-
out partial pivoting.
SUB GaussJordan(aug, m, n, x)
DOFOR k = 1, m
d = aug(k, k)
DOFOR j = 1, n
aug(k, j) = aug(k, j)/d
END DO
DOFOR 1 = 1, m
IF 1 % K THEN
d = aug(i, k)
DOFOR j = k, n
aug(1, j)
END DO
aug(1, j) - d*aug(k, j)
END IF
END DO
END DO
DOFOR k = 1, m
x(k) = aug(k, n)
END DO
END GaussJordan
11.9 Recall from Prob. 10.8, that the following system of equations
is designed to determine concentrations (the e's in g/m³) in a series
of coupled reactors as a function of amount of mass input to each
reactor (the right-hand sides are in g/day):
15c3cc33300
-3c18c26c3 = 1200
-4c₁₂+12c3 = 2400
Solve this problem with the Gauss-Seidel method to & = 5%.
9.8 Given the equations
10x+2x2-x3 = 27
-3x-6x2+2x3 = -61.5
x1 + x2 + 5x3 = -21.5
(a) Solve by naive Gauss elimination. Show all steps of the compu-
tation.
(b) Substitute your results into the original equations to check your
answers.
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 - 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. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - In Problems 11-14, a function and its graph are...Ch. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Find the relative maxima, relative minima, and...Ch. 10.2 - Find the relative maxima, relative minima, and...Ch. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 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 - 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. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 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. 39ECh. 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 - 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. 13ECh. 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. 18ECh. 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. 24ECh. 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 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.3 - Prob. 49ECh. 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 - Minimum cost A rectangular field with one side...Ch. 10.4 - Prob. 18ECh. 10.4 - 19. Optimization at a fixed cost A rectangular...Ch. 10.4 - Minimum cost A kennel of 640 square feet is to be...Ch. 10.4 - Minimum cost The base of a rectangular box is to...Ch. 10.4 - Prob. 22ECh. 10.4 - 23. Inventory cost model Suppose that a company...Ch. 10.4 - Inventory cost model Suppose that a company needs...Ch. 10.4 - Inventory cost model A company needs 150,000 items...Ch. 10.4 - Inventory cost model A company needs 450,000 items...Ch. 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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