MATHEMATICAL APPLICATIONS FOR THE MGT
12th Edition
ISBN: 9780357865095
Author: HARSHBARGER
Publisher: CENGAGE L
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Chapter 13.2, Problem 7E
To determine
To calculate: The value of the
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Suppose we have a linear program in standard equation form
maximize cTx
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.
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
x2 x3
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-2 0
1 1 0
0
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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
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0-4
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Rand No.
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ALASKA
0.372999976
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0.941323044
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4 ARKANSAS
0.071266381
Random Sample
CALIFORNIA
NORTH CAROLINA
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WASHINGTON
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Microsoft Excel snapshot for systematic sampling:
xfx INDEX(SD52:50551, F7)
A
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No.
States
Rand No. Random Sample
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0.4493186 OKLAHOMA
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3 ARIZONA
0.707914 KANSAS
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4 ARKANSAS 0.4831379 NORTH DAKOTA
6
5 CALIFORNIA 0.7277162 INDIANA
Random Sample
Sample Name
7
6 COLORADO 0.5865002 MISSISSIPPI
8
7:ONNECTICU 0.7640596 ILLINOIS
9
8 DELAWARE 0.5783029 MISSOURI
525
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15
INDIANA
MARYLAND
COLORADO
Chapter 13 Solutions
MATHEMATICAL APPLICATIONS FOR THE MGT
Ch. 13.1 - CHECKPOINT
1. For the interval [0, 2]. determine...Ch. 13.1 - Prob. 2CPCh. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - Prob. 8E
Ch. 13.1 - Prob. 9ECh. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - In Problems 14-19, find the value of each sum.
15....Ch. 13.1 - Prob. 16ECh. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Prob. 29ECh. 13.1 - Prob. 30ECh. 13.1 - Prob. 31ECh. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.1 - Prob. 35ECh. 13.1 - 36. Speed trials The figure gives the time it...Ch. 13.1 - Prob. 37ECh. 13.1 - 38. Drug levels in the blood The manufacturer of a...Ch. 13.1 - Prob. 39ECh. 13.1 - Prob. 40ECh. 13.2 - CHECKPOINT
1. True or false:
(a) For any integral,...Ch. 13.2 - Prob. 2CPCh. 13.2 - Evaluate the definite integrals in Problems...Ch. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Evaluate the definite integrals in Problems...Ch. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Evaluate the definite integrals in Problems...Ch. 13.2 - Evaluate the definite integrals in Problems...Ch. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Prob. 24ECh. 13.2 - Evaluate the definite integrals in Problems...Ch. 13.2 - Prob. 26ECh. 13.2 - Evaluate the definite integrals in Problems...Ch. 13.2 - Prob. 28ECh. 13.2 - Prob. 29ECh. 13.2 - Prob. 30ECh. 13.2 - Prob. 31ECh. 13.2 - Evaluate the definite integrals in Problems...Ch. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - Prob. 35ECh. 13.2 - Prob. 36ECh. 13.2 - Prob. 37ECh. 13.2 - Prob. 38ECh. 13.2 - In Problems 39-42, (a) write the integral that...Ch. 13.2 - Prob. 40ECh. 13.2 - In Problems 39-42, (a) write the integral that...Ch. 13.2 - In Problems 39-42, (a) write the integral that...Ch. 13.2 - Prob. 43ECh. 13.2 - 44. Find the area between the curve and the...Ch. 13.2 - Prob. 45ECh. 13.2 - 46. Find the area between the curve and the...Ch. 13.2 - Prob. 47ECh. 13.2 - Prob. 48ECh. 13.2 - Prob. 49ECh. 13.2 - Prob. 50ECh. 13.2 - Prob. 51ECh. 13.2 - Prob. 52ECh. 13.2 - Prob. 53ECh. 13.2 - Prob. 54ECh. 13.2 - 55. Depreciation The rate of depreciation of a...Ch. 13.2 - 56. Depreciation The rate of depreciation of a...Ch. 13.2 - 57. Sales and advertising A store finds that its...Ch. 13.2 - 58. Health care costs The U.S. total annual health...Ch. 13.2 - 59. Total income The income from an oil change...Ch. 13.2 - 60. Total income Suppose that a vending machine...Ch. 13.2 - Prob. 61ECh. 13.2 - Prob. 62ECh. 13.2 - Prob. 63ECh. 13.2 - Prob. 64ECh. 13.2 - Prob. 65ECh. 13.2 - Prob. 66ECh. 13.2 - 67. Testing The time t (in minutes) needed to read...Ch. 13.2 - 68. Response time In a small city, the response...Ch. 13.2 - Prob. 69ECh. 13.2 - 70. Product life The useful life of a car battery...Ch. 13.2 - Prob. 71ECh. 13.2 - 72. Psychology In a study of intelligence, the...Ch. 13.3 - CHECKPOINT
1. True or false:
(a) Over the interval...Ch. 13.3 - Prob. 2CPCh. 13.3 - Prob. 3CPCh. 13.3 - For each shaded region in Problems 1-6, (a) form...Ch. 13.3 - For each shaded region in Problems 1-6, (a) form...Ch. 13.3 - For each shaded region in Problems 1-6, (a) form...Ch. 13.3 - For each shaded region in Problems 1-6, (a) form...Ch. 13.3 - Prob. 5ECh. 13.3 - For each shaded region in Problems 1-6, (a) form...Ch. 13.3 - For each shaded region in Problems 7-12, (a) find...Ch. 13.3 - For each shaded region in Problems 7-12, (a) find...Ch. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - For each shaded region in Problems 7-12, (a) find...Ch. 13.3 - Prob. 12ECh. 13.3 - In Problems 13-26, equations are given whose...Ch. 13.3 - Prob. 14ECh. 13.3 - In Problems 13-26, equations are given whose...Ch. 13.3 - Prob. 16ECh. 13.3 - Prob. 17ECh. 13.3 - Prob. 18ECh. 13.3 - Prob. 19ECh. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13.3 - In Problems 13-26, equations are given whose...Ch. 13.3 - Prob. 25ECh. 13.3 - Prob. 26ECh. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - Prob. 29ECh. 13.3 - In Problems 27-32, find the average value of each...Ch. 13.3 - Prob. 31ECh. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - Prob. 34ECh. 13.3 - Prob. 35ECh. 13.3 - 36. Sales and advertising The figure shows the...Ch. 13.3 - Prob. 37ECh. 13.3 - 38. Inventory management The figure shows how an...Ch. 13.3 - 39. Sales and advertising The number of daily...Ch. 13.3 - 40. Demand The demand function for a certain...Ch. 13.3 - 41. Social Security beneficiaries With data from...Ch. 13.3 - Prob. 42ECh. 13.3 - Prob. 43ECh. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - 46. Income distribution In an effort to make the...Ch. 13.3 - Prob. 47ECh. 13.3 - Prob. 48ECh. 13.3 - Prob. 49ECh. 13.3 - Prob. 50ECh. 13.4 - CHECKPOINT
1. Suppose that a continuous income...Ch. 13.4 - Prob. 2CPCh. 13.4 - CHECKPOINT
3. If demand is , supply is , and the...Ch. 13.4 - 1. Find the total income over the next 10 years...Ch. 13.4 - 2. Find the total income over the next 8 years...Ch. 13.4 - 3. Suppose that a steel company views the...Ch. 13.4 - 4. Suppose that the Quick-Fix Car Service...Ch. 13.4 - 5. A small brewery considers the output of its...Ch. 13.4 - 6. A company that services a number of vending...Ch. 13.4 - 7. A franchise models the profit from its store as...Ch. 13.4 - 8. The Medi Spa franchise has a continuous income...Ch. 13.4 - 9. A continuous income stream has an annual rate...Ch. 13.4 - 10. A continuous income stream has an annual rate...Ch. 13.4 - 11. The income from an established chain of...Ch. 13.4 - Prob. 12ECh. 13.4 - 13. Suppose that a printing firm considers its...Ch. 13.4 - 14. Suppose that a vending machine company is...Ch. 13.4 - 15. A 58-year-old couple are considering opening a...Ch. 13.4 - Prob. 16ECh. 13.4 - Prob. 17ECh. 13.4 - Prob. 18ECh. 13.4 - In Problems 17-26, p and C are in dollars and x is...Ch. 13.4 - Prob. 20ECh. 13.4 - Prob. 21ECh. 13.4 - Prob. 22ECh. 13.4 - In Problems 17-26, p and C are in dollars and x is...Ch. 13.4 - Prob. 24ECh. 13.4 - In Problems 17-26, p and C are in dollars and x is...Ch. 13.4 - Prob. 26ECh. 13.4 - 27. Suppose that the supply function for a good...Ch. 13.4 - Prob. 28ECh. 13.4 - 29. If the supply function for a commodity is ,...Ch. 13.4 - Prob. 30ECh. 13.4 - Find the producers surplus at market equilibrium...Ch. 13.4 - 32. Find the producer's surplus at market...Ch. 13.4 - Prob. 33ECh. 13.4 - Prob. 34ECh. 13.4 - 35. The demand function for a certain product is ...Ch. 13.4 - Prob. 36ECh. 13.5 - Prob. 1CPCh. 13.5 - Prob. 2CPCh. 13.5 - Prob. 3CPCh. 13.5 - Prob. 4CPCh. 13.5 - Prob. 5CPCh. 13.5 - Prob. 6CPCh. 13.5 - Prob. 1ECh. 13.5 - Prob. 2ECh. 13.5 - Prob. 3ECh. 13.5 - Prob. 4ECh. 13.5 - Prob. 5ECh. 13.5 - Prob. 6ECh. 13.5 - Prob. 7ECh. 13.5 - Prob. 8ECh. 13.5 - Prob. 9ECh. 13.5 - Prob. 10ECh. 13.5 - Prob. 11ECh. 13.5 - Prob. 12ECh. 13.5 - Prob. 13ECh. 13.5 - Prob. 14ECh. 13.5 - Prob. 15ECh. 13.5 - Prob. 16ECh. 13.5 - Prob. 17ECh. 13.5 - Prob. 18ECh. 13.5 - Evaluate the integrals in Problems 1-32. Identify...Ch. 13.5 - Prob. 20ECh. 13.5 - Prob. 21ECh. 13.5 - Prob. 22ECh. 13.5 - Prob. 23ECh. 13.5 - Prob. 24ECh. 13.5 - Prob. 25ECh. 13.5 - Prob. 26ECh. 13.5 - Prob. 27ECh. 13.5 - Prob. 28ECh. 13.5 - Prob. 29ECh. 13.5 - Prob. 30ECh. 13.5 - Prob. 31ECh. 13.5 - Prob. 32ECh. 13.5 - Prob. 33ECh. 13.5 - Prob. 34ECh. 13.5 - Prob. 35ECh. 13.5 - Prob. 36ECh. 13.5 - Prob. 37ECh. 13.5 - Prob. 38ECh. 13.5 - Prob. 39ECh. 13.5 - Prob. 40ECh. 13.5 - 41. Income streams Suppose that when a new oil...Ch. 13.5 - Prob. 42ECh. 13.6 - Prob. 1CPCh. 13.6 - Prob. 2CPCh. 13.6 - Prob. 1ECh. 13.6 - Prob. 2ECh. 13.6 - Prob. 3ECh. 13.6 - Prob. 4ECh. 13.6 - Prob. 5ECh. 13.6 - Prob. 6ECh. 13.6 - Prob. 7ECh. 13.6 - Prob. 8ECh. 13.6 - Prob. 9ECh. 13.6 - Prob. 10ECh. 13.6 - Prob. 11ECh. 13.6 - In Problems 1-16, use integration by parts to...Ch. 13.6 - Prob. 13ECh. 13.6 - Prob. 14ECh. 13.6 - Prob. 15ECh. 13.6 - Prob. 16ECh. 13.6 - Prob. 17ECh. 13.6 - Prob. 18ECh. 13.6 - Prob. 19ECh. 13.6 - Prob. 20ECh. 13.6 - Prob. 21ECh. 13.6 - Prob. 22ECh. 13.6 - Prob. 23ECh. 13.6 - Prob. 24ECh. 13.6 - Prob. 25ECh. 13.6 - Prob. 26ECh. 13.6 - Prob. 27ECh. 13.6 - Prob. 28ECh. 13.6 - Prob. 29ECh. 13.6 - Prob. 30ECh. 13.6 - Prob. 31ECh. 13.6 - Prob. 32ECh. 13.6 - Prob. 33ECh. 13.6 - Prob. 34ECh. 13.6 - Prob. 35ECh. 13.6 - Prob. 36ECh. 13.6 - Prob. 37ECh. 13.6 - Prob. 38ECh. 13.7 - Prob. 1CPCh. 13.7 - Prob. 2CPCh. 13.7 - In Problems 1-20, evaluate the improper integrals...Ch. 13.7 - Prob. 2ECh. 13.7 - In Problems 1-20, evaluate the improper integrals...Ch. 13.7 - Prob. 4ECh. 13.7 - Prob. 5ECh. 13.7 - Prob. 6ECh. 13.7 - Prob. 7ECh. 13.7 - Prob. 8ECh. 13.7 - Prob. 9ECh. 13.7 - Prob. 10ECh. 13.7 - Prob. 11ECh. 13.7 - Prob. 12ECh. 13.7 - Prob. 13ECh. 13.7 - Prob. 14ECh. 13.7 - Prob. 15ECh. 13.7 - Prob. 16ECh. 13.7 - Prob. 17ECh. 13.7 - Prob. 18ECh. 13.7 - Prob. 19ECh. 13.7 - Prob. 20ECh. 13.7 - Prob. 21ECh. 13.7 - 22. For what value of c does
Ch. 13.7 - Prob. 23ECh. 13.7 - Prob. 24ECh. 13.7 - Prob. 25ECh. 13.7 - Prob. 26ECh. 13.7 - Prob. 27ECh. 13.7 - Prob. 28ECh. 13.7 - Prob. 29ECh. 13.7 - Prob. 30ECh. 13.7 - 31. Find the value of c so that
is a probability...Ch. 13.7 - Prob. 32ECh. 13.7 - Prob. 33ECh. 13.7 - Prob. 34ECh. 13.7 - 35. Find the area below the graph of and above...Ch. 13.7 - Prob. 36ECh. 13.7 - Prob. 37ECh. 13.7 - 38. Capital value Suppose that a donor wants to...Ch. 13.7 - 39. Capital value Suppose that a business provides...Ch. 13.7 - Prob. 40ECh. 13.7 - Prob. 41ECh. 13.7 - 42. Capital value Suppose that a business provides...Ch. 13.7 - 43. Repair time In a manufacturing process...Ch. 13.7 - 44. Customer service The duration t (in minutes)...Ch. 13.7 - Prob. 45ECh. 13.7 - 46. Warranties A manufacturer of electrical...Ch. 13.7 - Prob. 47ECh. 13.7 - Prob. 48ECh. 13.7 - Prob. 49ECh. 13.7 - 50. Inventory management A company uses wood chips...Ch. 13.8 - CHECKPOINT
1. Suppose [1, 4] is divided into 6...Ch. 13.8 - Prob. 2CPCh. 13.8 - Prob. 3CPCh. 13.8 - Prob. 1ECh. 13.8 - Prob. 2ECh. 13.8 - Prob. 3ECh. 13.8 - Prob. 4ECh. 13.8 - Prob. 5ECh. 13.8 - Prob. 6ECh. 13.8 - Prob. 7ECh. 13.8 - Prob. 8ECh. 13.8 - Prob. 9ECh. 13.8 - Prob. 10ECh. 13.8 - Prob. 11ECh. 13.8 - Prob. 12ECh. 13.8 - Prob. 13ECh. 13.8 - Prob. 14ECh. 13.8 - Prob. 15ECh. 13.8 - Prob. 16ECh. 13.8 - Prob. 17ECh. 13.8 - Prob. 18ECh. 13.8 - Prob. 19ECh. 13.8 - Prob. 20ECh. 13.8 - Prob. 21ECh. 13.8 - Prob. 22ECh. 13.8 - In Problems 23-30, round all calculations to 2...Ch. 13.8 - In Problems 23-30, round all calculations to 2...Ch. 13.8 - Prob. 25ECh. 13.8 - Prob. 26ECh. 13.8 - In Problems 23-30, round all calculations to 2...Ch. 13.8 - In Problems 23-30, round all calculations to 2...Ch. 13.8 - Prob. 29ECh. 13.8 - Prob. 30ECh. 13.8 - Prob. 31ECh. 13.8 - Prob. 32ECh. 13.8 - 33. Pollution monitoring Suppose that the presence...Ch. 13.8 - Prob. 34ECh. 13 - 1. Calculate .
Ch. 13 - 2. Use formulas to simplify
Ch. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - 5. Use a definite integral to find the area under...Ch. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - Prob. 16RECh. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Prob. 20RECh. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - Prob. 23RECh. 13 - Prob. 24RECh. 13 - Prob. 25RECh. 13 - Prob. 26RECh. 13 - Prob. 27RECh. 13 - Prob. 28RECh. 13 - Prob. 29RECh. 13 - In Problems 27-30, use integration by parts to...Ch. 13 - Prob. 31RECh. 13 - Prob. 32RECh. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - Prob. 35RECh. 13 - Prob. 36RECh. 13 - Prob. 37RECh. 13 - 38. Use the table that follows to...Ch. 13 - 39. Suppose that a definite integral is to be...Ch. 13 - 40. Maintenance Maintenance costs for buildings...Ch. 13 - Prob. 41RECh. 13 - Prob. 42RECh. 13 - Prob. 43RECh. 13 - Prob. 44RECh. 13 - Prob. 45RECh. 13 - 46. Income streams Suppose that a machine’s...Ch. 13 - Prob. 47RECh. 13 - Prob. 48RECh. 13 - Prob. 49RECh. 13 - Prob. 50RECh. 13 - Prob. 51RECh. 13 - Prob. 52RECh. 13 - 53. Quality control The length of time (in years)...Ch. 13 - 54. Capital value Find the capital value of a...Ch. 13 - 55. Total income Suppose that a continuous income...Ch. 13 - Prob. 56RECh. 13 - 1. Use left-hand endpoints and subdivisions to...Ch. 13 - 2. Consider from with n equal subdivisions.
(a)...Ch. 13 - Prob. 3TCh. 13 - Prob. 4TCh. 13 - Prob. 5TCh. 13 - Prob. 6TCh. 13 - Prob. 7TCh. 13 - Prob. 8TCh. 13 - 9. Suppose the supply function for a product is ...Ch. 13 - 10. Suppose a continuous income stream has an...Ch. 13 - Prob. 11TCh. 13 - Prob. 12TCh. 13 - Prob. 13TCh. 13 - Prob. 14TCh. 13 - Prob. 15TCh. 13 - 16. The environmental effects of a chemical spill...
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