Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
6th Edition
ISBN: 9780321914620
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Chapter 8.A, Problem 20E
To determine
To compare: The Total world harvest of all grains to the total weight of wheat on the chessboard.
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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 8 Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Ch. 8.A - Prob. 1QQCh. 8.A - Prob. 2QQCh. 8.A - The balance owed your credit card doubles from...Ch. 8.A - The number Of songs in your iPod has increased...Ch. 8.A - Which of the following is in example of...Ch. 8.A - On a chessboard with 64 squares, you place 1 penny...Ch. 8.A - At 11:00 you place a single bacterium in a bottle,...Ch. 8.A - Consider the bacterial population described in...Ch. 8.A - Consider the bacterial population described in...Ch. 8.A - Which of the following is not true of any...
Ch. 8.A - Describe basic differences between linear growth...Ch. 8.A - 2. Briefly explain how repeated doublings...Ch. 8.A - Briefly summarize the Story Of the bacteria in the...Ch. 8.A - Explain the meaning Of the two key facts about...Ch. 8.A - Prob. 5ECh. 8.A - Suppose you had a magic hank account in which your...Ch. 8.A - A small town that grows exponentially can become a...Ch. 8.A - H. Human population has been growing exponentially...Ch. 8.A - Prob. 9ECh. 8.A - Prob. 10ECh. 8.A - Prob. 11ECh. 8.A - Prob. 12ECh. 8.A - Prob. 13ECh. 8.A - Prob. 14ECh. 8.A - Linear or Exponential? State whether the growth...Ch. 8.A - Prob. 16ECh. 8.A - Chessboard Parable. Use the chessboard parable...Ch. 8.A - Chessboard Parable. Use the chessboard parable...Ch. 8.A - Chessboard Parable. Use the chessboard parable...Ch. 8.A - Prob. 20ECh. 8.A - Magic Penny Parable. Use the magic penny parable...Ch. 8.A - Prob. 22ECh. 8.A - Magic Penny Parable. Use the magic penny parable...Ch. 8.A - Magic Penny Parable. Use the magic penny parable...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - Bacteria in a Bottle Parable. Use the bacteria...Ch. 8.A - 29. Human Doubling. Human population in the year...Ch. 8.A - Doubling Time versus Initial Amount. a. Would you...Ch. 8.A - Facebook Users. The table shows the number of...Ch. 8.A - Prob. 32ECh. 8.A - Exponential Growth. Identify at least two news...Ch. 8.A - Prob. 34ECh. 8.A - Prob. 35ECh. 8.B - Prob. 1QQCh. 8.B - Prob. 2QQCh. 8.B - Which of the following is not a good approximation...Ch. 8.B - Prob. 4QQCh. 8.B - Radioactive tritium (hvdrogen-3) has a halt-life...Ch. 8.B - Radioactive uramum-235 has a hall-life of about...Ch. 8.B - Prob. 7QQCh. 8.B - log10108= a.100,000,000 b. 108 c.8Ch. 8.B - A rural popular ion decreases at a rate of 20% per...Ch. 8.B - Prob. 10QQCh. 8.B - What is a doubling tune? Suppose a population has...Ch. 8.B - Prob. 2ECh. 8.B - State the approximate doubting time formula and...Ch. 8.B - Prob. 4ECh. 8.B - Prob. 5ECh. 8.B - 6. State the approximate hall-life formula and the...Ch. 8.B - 7. Briefly describe exact doubling time and...Ch. 8.B - 8. Give an example in which it is important to use...Ch. 8.B - Our town is growing with a doubling time of 25...Ch. 8.B - Our town is growing at a rate of 7% per year, so...Ch. 8.B - A toxic chemical decays with a hall-life of 10...Ch. 8.B - The hall-life of plutomum-239 is about 24,000...Ch. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Prob. 15ECh. 8.B - Prob. 16ECh. 8.B - 13-24: Logarithms. Refer to the Brief Review on p....Ch. 8.B - Prob. 18ECh. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - 13-24: Logarithms. Refer to the Brief Review on p....Ch. 8.B - Prob. 22ECh. 8.B - Prob. 23ECh. 8.B - Logarithms. Refer to the Brief Review on p. 488....Ch. 8.B - Prob. 25ECh. 8.B - Prob. 26ECh. 8.B - Prob. 27ECh. 8.B - Prob. 28ECh. 8.B - Prob. 29ECh. 8.B - Prob. 30ECh. 8.B - Prob. 31ECh. 8.B - Prob. 32ECh. 8.B - Prob. 33ECh. 8.B - Prob. 34ECh. 8.B - 31. Rabbits. A community of rabbits begins with an...Ch. 8.B - Prob. 36ECh. 8.B - Doubling Time Formula. Use the approximate...Ch. 8.B - Prob. 38ECh. 8.B - Prob. 39ECh. 8.B - Prob. 40ECh. 8.B - Prob. 41ECh. 8.B - Prob. 42ECh. 8.B - Prob. 43ECh. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - Prob. 45ECh. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - Prob. 47ECh. 8.B - 41 -48: Half-Life. Each exercise gives a half-life...Ch. 8.B - Prob. 49ECh. 8.B - 49-52: Half-Life Formula. Use the approximate...Ch. 8.B - Prob. 51ECh. 8.B - 49-52: Half-Life Formula. Use the approximate...Ch. 8.B - Prob. 53ECh. 8.B - Exact Formulas. Compare the doubling times found...Ch. 8.B - Prob. 55ECh. 8.B - Exact Formulas. Compare the doubling times found...Ch. 8.B - Prob. 57ECh. 8.B - 58. Nuclear Weapons. Thermonuclear weapons use...Ch. 8.B - Fossil Fuel Emissions. Total emissions of carbon...Ch. 8.B - Yucca Mountain. The U.S. government spent nearly...Ch. 8.B - Crime Rate. The homicide rate decreases at a rate...Ch. 8.B - 62. Drug Metabolism. A particular antibiotic is...Ch. 8.B - Atmospheric Pressure. The pressure of Earth's...Ch. 8.B - Prob. 64ECh. 8.B - 65. Radioactive Half-Life. Find a news story that...Ch. 8.B - Prob. 66ECh. 8.B - Prob. 67ECh. 8.B - Prob. 68ECh. 8.B - Prob. 69ECh. 8.C - Prob. 1QQCh. 8.C - Prob. 2QQCh. 8.C - The primary reason for the rapid growth of human...Ch. 8.C - The carrying capacity of the Earth is defined as...Ch. 8.C - Which of the billowing would cause estimates of...Ch. 8.C - 6. Recall the bacteria in a bottle example from...Ch. 8.C - When researchers project that human population...Ch. 8.C - Prob. 8QQCh. 8.C - Prob. 9QQCh. 8.C - Prob. 10QQCh. 8.C - Based on Figure 8.3, contrast the changes in human...Ch. 8.C - Prob. 2ECh. 8.C - Haw do today’s birth and death rates compare to...Ch. 8.C - Prob. 4ECh. 8.C - Prob. 5ECh. 8.C - What is overshot and collapse? Under what...Ch. 8.C - Prob. 7ECh. 8.C - 8. If birth rates fall more than death rates, the...Ch. 8.C - The carrying capacity of our planet depends only...Ch. 8.C - to rapid increases in computing technology, we...Ch. 8.C - In the wild, we always expect the population of...Ch. 8.C - Prob. 12ECh. 8.C - Prob. 13ECh. 8.C - Varying Growth Rates. Starting from a 2013...Ch. 8.C - Prob. 15ECh. 8.C - 13-16: Varying Growth Rates. Starting from a 2013...Ch. 8.C - Birth and Death Rates. The following table gives...Ch. 8.C - Prob. 18ECh. 8.C - Prob. 19ECh. 8.C - Prob. 20ECh. 8.C - 21. Logistic Growth. Consider a population that...Ch. 8.C - Logistic Growth. Consider a population that begins...Ch. 8.C - Prob. 23ECh. 8.C - Prob. 24ECh. 8.C - Prob. 25ECh. 8.C - Prob. 26ECh. 8.C - Prob. 27ECh. 8.C - Prob. 28ECh. 8.C - Prob. 29ECh. 8.C - Prob. 30ECh. 8.C - Prob. 31ECh. 8.C - Prob. 32ECh. 8.C - Prob. 33ECh. 8.C - Prob. 34.0ECh. 8.C - Prob. 34.1ECh. 8.C - Population Predictions. Find population...Ch. 8.C - Prob. 36ECh. 8.C - Prob. 37ECh. 8.C - Prob. 38ECh. 8.C - Prob. 39ECh. 8.D - The energy release of a magnitude 7 earthquake is...Ch. 8.D - Prob. 2QQCh. 8.D - 3. What is a 0-decibel sound?
the softest sound...Ch. 8.D - Prob. 4QQCh. 8.D - Prob. 5QQCh. 8.D - Prob. 6QQCh. 8.D - Prob. 7QQCh. 8.D - Prob. 8QQCh. 8.D - Prob. 9QQCh. 8.D - Prob. 10QQCh. 8.D - What is the magnitude scale for earthquakes? What...Ch. 8.D - What is the decibel scale? Describe how it is...Ch. 8.D - What is pH? What pH values define an acid, a base,...Ch. 8.D - What is acid rain? Why is it a serious...Ch. 8.D - 5. An earthquake of magnitude 8 will do twice as...Ch. 8.D - A 120-dB wand is 20% louder than a 100-dB sound.Ch. 8.D - If I double the amount of water in the cup, I'll...Ch. 8.D - The lake water was crystal clear, so It could not...Ch. 8.D - Earthquake Magnitudes. Use the earthquake...Ch. 8.D - Prob. 10ECh. 8.D - Prob. 11ECh. 8.D - Earthquake Magnitudes. Use the earthquake...Ch. 8.D - Earthquake Magnitudes. Use the earthquake...Ch. 8.D - 9-14: Earthquake Magnitudes. Use the earthquake...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - The Decibel Scale. Use the decibel scale to answer...Ch. 8.D - Prob. 20ECh. 8.D - Inverse Square Law. Use the inverse square law for...Ch. 8.D - Prob. 22ECh. 8.D - Inverse Square Law. Use the inverse square law for...Ch. 8.D - Inverse Square Law. Use the inverse square law for...Ch. 8.D - The pH scale. Use the pH scale to answer the...Ch. 8.D - The pH Scale. Use the pH scale to answer the...Ch. 8.D - Prob. 27ECh. 8.D - Prob. 28ECh. 8.D - Prob. 29ECh. 8.D - Prob. 30ECh. 8.D - The pH Scale. Use the pH scale to answer the...Ch. 8.D - 25-32: The pH Scale. Use the pH scale to answer...Ch. 8.D - Logarithmic Thinking. Briefly describe, in words,...Ch. 8.D - 33-38: Logarithmic Thinking. Briefly describe, in...Ch. 8.D - Logarithmic Thinking. Briefly describe, in words,...Ch. 8.D - Logarithmic Thinking. Briefly describe, in words,...Ch. 8.D - Prob. 37ECh. 8.D - Prob. 38ECh. 8.D - 39. Sound and Distance.
The decibel level for...Ch. 8.D - 40. Variation in Sound with Distance. Suppose that...Ch. 8.D - Toxic Dumping in Acidified Lakes. Consider a...Ch. 8.D - Earthquakes in the News. Find a recent news story...Ch. 8.D - Prob. 43ECh. 8.D - Disasters. Find the death lolls for some of the...Ch. 8.D - Prob. 45E
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