Mathematical Applications for the Management, Life, and Social Sciences
12th Edition
ISBN: 9781337625340
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 10, Problem 17RE
(a)
To determine
To calculate: The absolute maximum and minimum for R for the expression
(b)
To determine
To calculate: The absolute maximum and minimum for the expression
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Client
1
Weight before
diet (pounds)
Weight after
diet (pounds)
128
120
2
131
123
3
140
141
4
178
170
5
121
118
6
136
136
7
118
121
8
136
127
a) Determine the mean change in patient weight from before to after the
diet (after – before). What is the 95% confidence interval of this mean
difference?
You manage a chemical company with 2 warehouses. The following quantities of
Important Chemical A have arrived from an international supplier at 3 different
ports:
Chemical Available (L)
Port 1
Port 2
Port 3
400
110
100
The following amounts of Important Chemical A are required at your warehouses:
Warehouse 1
Warehouse 2
Chemical Required (L)
380
230
The cost in £ to ship 1L of chemical from each port to each warehouse is as follows:
Warehouse 1 Warehouse 2
Port 1
£10
£45
Port 2
£20
£28
Port 3
£13
£11
(a) You want to know how to send these shipments as cheaply as possible. For-
mulate this as a linear program (you do not need to formulate it in standard
inequality form) indicating what each variable represents.
a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in
standard inequality form (with 3 variables and 4 constraints) and suppose that we have
reached a point where we have obtained the following tableau. Apply one more pivot
operation, indicating the highlighted row and column and the row operations you carry
out. What can you conclude from your updated tableau?
x1 12 23
81
82
83
S4
$1
-20
1 1
0
0
0
3
82
3 0
-2
0
1
2
0
6
12
1
1
-3
0
0
1
0
2
84
-3 0
2
0
0
-1 1 4
2
-2
0 11
0
0
-4
0
-8
b) Solve the following linear program using the 2-phase simplex algorithm. You should give
the initial tableau and each further tableau produced during the execution of the
algorithm. If the program has an optimal solution, give this solution and state its
objective value. If it does not have an optimal solution, say why.
maximize 21 - - 2x2 + x3 - 4x4
subject to 2x1+x22x3x4≥ 1,
5x1+x2-x3-4 -1,
2x1+x2-x3-342,
1, 2, 3, 4 ≥0.
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Suppose we have a linear program in standard equation form maximize c'x subject to Ax=b, x≥ 0. and suppose u, v, and w are all optimal solutions to this linear program. (a) Prove that zu+v+w is an optimal solution. (b) If you try to adapt your proof from part (a) to prove that that u+v+w is an optimal solution, say exactly which part(s) of the proof go wrong. (c) If you try to adapt your proof from part (a) to prove that u+v-w is an optimal solution, say exactly which part(s) of the proof go wrong.arrow_forward(a) For the following linear programme, sketch the feasible region and the direction of the objective function. Use you sketch to find an optimal solution to the program. State the optimal solution and give the objective value for this solution. maximize +22 subject to 1 + 2x2 ≤ 4, 1 +3x2 ≤ 12, x1, x2 ≥0 (b) For the following linear programme, sketch the feasible region and the direction of the objective function. Explain, making reference to your sketch, why this linear programme is unbounded. maximize ₁+%2 subject to -2x1 + x2 ≤ 4, x1 - 2x2 ≤4, x1 + x2 ≥ 7, x1,x20 Give any feasible solution to the linear programme for which the objective value is 40 (you do not need to justify your answer).arrow_forwardfind the domain of the function f(x)arrow_forward
- For each of the following functions, find the Taylor Series about the indicated center and also determine the interval of convergence for the series. 1. f(x) = ex-2, c = 2 Π == 2. f(x) = sin(x), c = 2arrow_forwardQUESTION 5. Show that if 0 ≤r≤n, then r+2 r r (c) + (+³) + (+³) +- + (*) -(+) n n+ = r (1)...using induction on n. (2) ...using a combinatorial proof.arrow_forwardUse a power series to approximate each of the following to within 3 decimal places: 1. arctan 2. In (1.01)arrow_forward
- For each of the following power series, find the interval of convergence and the radius of convergence: n² 1.0 (x + 1)" n=1 շո 3n 2. Σ n=1 (x-3)n n3arrow_forwardUse a known series to find a power series in x that has the given function as its sum: 1. xcos(x³) 2. In (1+x) xarrow_forwardif n is odd integer then 4 does not divide narrow_forward
- or W Annuities L Question 2, 5.3.7 > Find the future value for the ordinary annuity with the given payment and interest rate. PMT = $2,000; 1.65% compounded quarterly for 11 years. The future value of the ordinary annuity is $ (Do not round until the final answer. Then round to the nearest cent as needed.) example Get more help Q Search 30 Larrow_forwardFind the cdf of a random variable Y whose pdf is given by; 2, 0≤x≤1 1/3, 0≤x≤1 a) f(x)=3, 2≤x≤4 0, elsewhere 2, 1≤x≤2 b) f(x)= (3-x)2, 2≤x≤3 0, elsewherearrow_forwardFor all integers a and b, a + b is not ≡ 0(mod n) if and only if a is not ≡ 0(mod n)a or is not b ≡ 0(mod n). Is conjecture true or false?why?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY