MATHEMATICAL APPLICATIONS FOR THE MGT
12th Edition
ISBN: 9780357865095
Author: HARSHBARGER
Publisher: CENGAGE L
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Chapter 13.8, Problem 8E
(a)
To determine
To calculate: The approximate value of integral
(b)
To determine
To calculate: The approximate value of integral
(c)
To determine
To calculate: The exact value of
(d)
To determine
The most accurate approximation rule among the Trapezoidal rule and Simpson Rule.
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(c) Describe the distribution plan and show the total distribution cost.
Optimal Solution
Amount
Cost
$ 2000
Southern-Hamilton
200
Southern-Butler
$
Southern-Clermont
300
4500
Northwest-Hamilton
200
$2400
Northwest-Butler
200
$3000
Northwest-Clermont
$
Total Cost
ક
(d) Recent residential and industrial growth in Butler County has the potential for increasing demand by 100 units.
(i) Create an updated distribution plan assuming Southern Gas becomes the preferred supplier.
Distribution Plan with Southern Gas
Amount
Southern-Hamilton
$
Cost
×
Southern-Butler
x
$
Southern-Clermont
300
$ 4500
Northwest-Hamilton
64
x
Northwest-Butler
$
×
Northwest-Clermont 0
$0
Total Cost
$
(ii) Create an updated distribution plan assuming Northwest Gas becomes the preferred supplier.
Distribution Plan with Northwest Gas
Southern-Hamilton
Southern-Butler
0
Southern-Clermont
Northwest-Hamilton
Northwest-Butler
Northwest-Clermont
Total Cost
Amount
×
x
x
+7
$0
Cost
×
$
×
$
×
+4
$
-/+
$
×
×
The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows.
Warehouse
Plant
Capacity
1
2
1
4
7
450
2
8
5
600
3
5
6
380
Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows.
Customer
Warehouse
1
2 3
1
6
4
8
2
3
6
7
7
Demand
300 300 300 400
(a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.)
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(b) Formulate a linear programming model of the problem. (Let Plant 1 be node 1, Plant 2 be node 2, Plant 3 be node 3, Warehouse 1 be node 4, Warehouse 2 be node 5, Customer 1 be node 6, Customer 2 be node 7, Customer 3 be node 8, and Customer 4 be node 9. Express your answers in the form x;;, where x,; represents the number of units shipped from
node i to node j.)
Min 4x14+8x24+5x34+7x15 +5x25…
A linear programming computer package is needed.
Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Hanson increases its normal room rates and takes reservations based on a revenue management system. A large profesional organization has scheduled its annual convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its
rooms available for convention attendees at a special convention rate in order to be listed as a recommended hotel for the convention. Although the majority of attendees at the annual meeting typically request a Friday and Saturday two-night package, some attendees may select a Friday night only or a Saturday night only reservation. Customers not attending the convention may also request a Friday and
Saturday two-night package, or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are…
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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