Math in Our World
3rd Edition
ISBN: 9780073519678
Author: David Sobecki Professor, Allan G. Bluman
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 14.1, Problem 12E
How does graph coloring apply to maps?
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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 14 Solutions
Math in Our World
Ch. 14.1 - Draw a graph to represent ferry service between...Ch. 14.1 - The floor plan shown in Figure 14-7 is for a...Ch. 14.1 - Prob. 3TTOCh. 14.1 - Draw a graph for my neighborhood, shown in Figure...Ch. 14.1 - Prob. 5TTOCh. 14.1 - Prob. 6TTOCh. 14.1 - Prob. 7TTOCh. 14.1 - Prob. 8TTOCh. 14.1 - Prob. 1ECh. 14.1 - What is the difference between a loop and a...
Ch. 14.1 - What is the difference between a circuit and a...Ch. 14.1 - Draw two graphs that look physically different but...Ch. 14.1 - Prob. 5ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - Prob. 10ECh. 14.1 - Prob. 11ECh. 14.1 - How does graph coloring apply to maps?Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Prob. 18ECh. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Prob. 20ECh. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Use the following graph to answer Exercises 1324....Ch. 14.1 - Prob. 25ECh. 14.1 - Prob. 26ECh. 14.1 - Prob. 27ECh. 14.1 - Prob. 28ECh. 14.1 - Prob. 29ECh. 14.1 - Prob. 30ECh. 14.1 - For Exercises 3134, represent each figure using a...Ch. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.1 - Prob. 34ECh. 14.1 - Prob. 35ECh. 14.1 - Prob. 36ECh. 14.1 - For Exercises 3538, draw a graph to represent each...Ch. 14.1 - Prob. 38ECh. 14.1 - Prob. 39ECh. 14.1 - For Exercises 3942, draw a graph that represents...Ch. 14.1 - Prob. 41ECh. 14.1 - Prob. 42ECh. 14.1 - In Exercises 4350, use graph coloring to find the...Ch. 14.1 - Prob. 44ECh. 14.1 - Prob. 45ECh. 14.1 - Prob. 46ECh. 14.1 - In Exercises 4350, use graph coloring to find the...Ch. 14.1 - Prob. 48ECh. 14.1 - Prob. 49ECh. 14.1 - Prob. 50ECh. 14.1 - Prob. 51ECh. 14.1 - Prob. 52ECh. 14.1 - Prob. 53ECh. 14.1 - Prob. 54ECh. 14.1 - Prob. 55ECh. 14.1 - Draw a graph that represents the street map in...Ch. 14.1 - Prob. 57ECh. 14.1 - Prob. 58ECh. 14.1 - Prob. 59ECh. 14.1 - Prob. 61ECh. 14.1 - Prob. 62ECh. 14.1 - Prob. 63ECh. 14.1 - (a)When a graph represents a map as in Exercise...Ch. 14.2 - Use Eulers theorem to determine if the graphs...Ch. 14.2 - Prob. 2TTOCh. 14.2 - Prob. 3TTOCh. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - For Exercises 710, decide whether each connected...Ch. 14.2 - Prob. 8ECh. 14.2 - For Exercises 710, decide whether each connected...Ch. 14.2 - Prob. 10ECh. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - Prob. 12ECh. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - Prob. 14ECh. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - Prob. 16ECh. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - Prob. 18ECh. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - For Exercises 1120, (a)State whether the graph has...Ch. 14.2 - Prob. 21ECh. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - For Exercises 2126, draw a graph for the figures...Ch. 14.2 - Prob. 27ECh. 14.2 - Prob. 28ECh. 14.2 - Prob. 29ECh. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - For Exercises 33 and 34, determine if an Euler...Ch. 14.2 - For Exercises 33 and 34, determine if an Euler...Ch. 14.2 - Prob. 35ECh. 14.2 - Prob. 37ECh. 14.2 - Prob. 38ECh. 14.2 - Draw some sample graphs and use them to discuss...Ch. 14.2 - Prob. 40ECh. 14.2 - Prob. 41ECh. 14.2 - Prob. 42ECh. 14.2 - Explain why the word connected is crucial...Ch. 14.2 - Prob. 44ECh. 14.2 - Prob. 45ECh. 14.2 - Prob. 46ECh. 14.3 - Find a Hamilton path that begins at vertex C for...Ch. 14.3 - Prob. 2TTOCh. 14.3 - Prob. 3TTOCh. 14.3 - The driving times in minutes between four cities...Ch. 14.3 - Prob. 5TTOCh. 14.3 - Prob. 6TTOCh. 14.3 - Prob. 7TTOCh. 14.3 - What is the difference between a Hamilton path and...Ch. 14.3 - Prob. 2ECh. 14.3 - Give an example of a problem in our world that can...Ch. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Describe what a typical traveling salesperson...Ch. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.3 - For Exercises 1118, find two different Hamilton...Ch. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Prob. 14ECh. 14.3 - For Exercises 1118, find two different Hamilton...Ch. 14.3 - Prob. 16ECh. 14.3 - Prob. 17ECh. 14.3 - Prob. 18ECh. 14.3 - For Exercises 1118, find two different Hamilton...Ch. 14.3 - Prob. 20ECh. 14.3 - Prob. 21ECh. 14.3 - Prob. 22ECh. 14.3 - For Exercises 1924, find two different Hamilton...Ch. 14.3 - Prob. 24ECh. 14.3 - Prob. 25ECh. 14.3 - Prob. 26ECh. 14.3 - For Exercises 2528, find the number of Hamilton...Ch. 14.3 - Prob. 28ECh. 14.3 - Prob. 29ECh. 14.3 - For Exercises 29 and 30, use the brute force...Ch. 14.3 - For Exercises 3134, use the nearest neighbor...Ch. 14.3 - Prob. 32ECh. 14.3 - Prob. 33ECh. 14.3 - Prob. 34ECh. 14.3 - In Exercises 3538, use the cheapest link algorithm...Ch. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - Prob. 38ECh. 14.3 - Prob. 39ECh. 14.3 - For Exercises 3942, use the information in the...Ch. 14.3 - Prob. 41ECh. 14.3 - Prob. 42ECh. 14.3 - Prob. 43ECh. 14.3 - For Exercises 4346, use the information in the...Ch. 14.3 - For Exercises 4346, use the information in the...Ch. 14.3 - Prob. 46ECh. 14.3 - Prob. 47ECh. 14.3 - A pizza delivery person has five prearranged...Ch. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.3 - Prob. 51ECh. 14.3 - Prob. 52ECh. 14.3 - When planning routes, distance isnt always the key...Ch. 14.3 - Prob. 54ECh. 14.3 - Repeat questions 51 through 54, choosing four...Ch. 14.3 - Prob. 56ECh. 14.3 - Prob. 57ECh. 14.3 - Prob. 58ECh. 14.3 - Find a road atlas that has a mileage chart. Pick...Ch. 14.3 - Prob. 60ECh. 14.3 - Prob. 61ECh. 14.3 - Prob. 62ECh. 14.3 - Prob. 63ECh. 14.3 - Prob. 64ECh. 14.3 - Prob. 65ECh. 14.3 - Prob. 66ECh. 14.4 - Prob. 1TTOCh. 14.4 - Prob. 2TTOCh. 14.4 - Prob. 3TTOCh. 14.4 - Prob. 4TTOCh. 14.4 - Prob. 5TTOCh. 14.4 - Prob. 1ECh. 14.4 - Prob. 2ECh. 14.4 - Prob. 3ECh. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - Prob. 6ECh. 14.4 - For Exercise 716, decide whether or not each graph...Ch. 14.4 - Prob. 8ECh. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Prob. 24ECh. 14.4 - Prob. 25ECh. 14.4 - Prob. 26ECh. 14.4 - Prob. 27ECh. 14.4 - Prob. 28ECh. 14.4 - Prob. 29ECh. 14.4 - Prob. 30ECh. 14.4 - Prob. 31ECh. 14.4 - Prob. 32ECh. 14.4 - Prob. 33ECh. 14.4 - As a new suburban neighborhood is being built, the...Ch. 14.4 - Prob. 35ECh. 14.4 - Prob. 36ECh. 14.4 - Prob. 37ECh. 14.4 - Prob. 38ECh. 14.4 - Prob. 39ECh. 14.4 - In the last two sections, we used both Hamilton...Ch. 14.4 - Prob. 41ECh. 14.4 - Prob. 42ECh. 14 - Use the graph shown in Figure 14-62 for Exercise...Ch. 14 - Prob. 2RECh. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - Prob. 5RECh. 14 - Prob. 6RECh. 14 - Use the graph shown in Figure 14-62 for Exercises...Ch. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - Repeat Exercise 13 for the graphs from Exercises...Ch. 14 - Prob. 15RECh. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RECh. 14 - Prob. 22RECh. 14 - Prob. 23RECh. 14 - Prob. 24RECh. 14 - Prob. 25RECh. 14 - Prob. 26RECh. 14 - Prob. 27RECh. 14 - Prob. 28RECh. 14 - Prob. 29RECh. 14 - Prob. 30RECh. 14 - Prob. 31RECh. 14 - Prob. 32RECh. 14 - Prob. 33RECh. 14 - Prob. 34RECh. 14 - For the following graph: (a)What is the degree of...Ch. 14 - Draw a graph with two bridges, and the...Ch. 14 - Prob. 3CTCh. 14 - Prob. 4CTCh. 14 - (a)For the graph shown in Figure 14-73, find an...Ch. 14 - Prob. 6CTCh. 14 - For the housing plan shown in Figure 14-75, draw a...Ch. 14 - Prob. 8CTCh. 14 - Use the brute force method to find the shortest...Ch. 14 - Use the nearest neighbor method and cheapest link...Ch. 14 - Prob. 11CTCh. 14 - Decide whether the problem can be solved using...
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