Introductory Combinatorics
5th Edition
ISBN: 9780134689616
Author: Brualdi, Richard A.
Publisher: Pearson,
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Chapter 10, Problem 42E
To determine
To construct: Four MOLS of order 5.
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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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This answer has not been graded yet.
(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 10 Solutions
Introductory Combinatorics
Ch. 10 - Prob. 1ECh. 10 - Prob. 2ECh. 10 - Prob. 3ECh. 10 - Prob. 4ECh. 10 - Prove that no two integers in Zn, arithmetic mod...Ch. 10 - Prob. 6ECh. 10 - Prob. 7ECh. 10 - Prob. 8ECh. 10 - Prob. 9ECh. 10 - Determine which integers in Z12 have...
Ch. 10 - Prob. 11ECh. 10 - Prob. 12ECh. 10 - Let n = 2m + 1 be an odd integer with m ≥ 2. Prove...Ch. 10 - Use the algorithm in Section 10.1 to find the GCD...Ch. 10 - For each of the pairs of integers in Exercise 14,...Ch. 10 - Apply the algorithm for the GCD in Section 10.1 to...Ch. 10 - Start with the field Z2 and show that x3 + x + 1...Ch. 10 - Does there exist a BIBD with parameters b = 10, v...Ch. 10 - Prob. 19ECh. 10 - Prob. 20ECh. 10 - Determine the complementary design of the BIBD...Ch. 10 - Prob. 22ECh. 10 - How are the incidence matrices of a BIBD and its...Ch. 10 - Show that a BIBD, with v varieties whose block...Ch. 10 - Prove that a BIBD with parameters b, v, k, r, λ...Ch. 10 - Let B be a difference set in Zn. Show that, for...Ch. 10 - Prob. 27ECh. 10 - Show that B = {0, 1, 3, 9} is a difference set in...Ch. 10 - Prob. 29ECh. 10 - Prob. 30ECh. 10 - Prob. 31ECh. 10 - Prob. 32ECh. 10 - Let t be a positive integer. Use Theorem 10.3.2 to...Ch. 10 - Let t be a positive integer. Prove that, if there...Ch. 10 - Assume a Steiner triple system exists with...Ch. 10 - Prob. 36ECh. 10 - Prove that, if we interchange the rows of a Latin...Ch. 10 - Use the method in Theorem 10.4.2 with n = 6 and r...Ch. 10 - Let n be a positive integer and let r be a nonzero...Ch. 10 - Let n be a positive integer and let r and rʹ be...Ch. 10 - Use the method in Theorem 10.4.2 with n = 8 and r...Ch. 10 - Construct four MOLS of order 5.
Ch. 10 - Prob. 43ECh. 10 - Construct two MOLS of order 9.
Ch. 10 - Prob. 45ECh. 10 - Construct two MOLS of order 8.
Ch. 10 - Prob. 47ECh. 10 - Prob. 48ECh. 10 - Prob. 49ECh. 10 - Let A1 and A2 be MOLS of order m and let B1 and B2...Ch. 10 - Construct a completion of the 3-by-6 Latin...Ch. 10 - Prob. 53ECh. 10 - Prob. 54ECh. 10 - Prob. 55ECh. 10 - Prob. 56ECh. 10 - Prob. 57ECh. 10 - Prob. 58ECh. 10 - Prob. 59ECh. 10 - Prob. 60ECh. 10 - Let , where m is a positive integer. Prove that...
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