Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Transcribed Image Text:Consider the following network representation of a transportation problem.
45
25
Supplies
Jefferson
City
Omaha
15
10
00
8
8
11
25
Des Moines
Kansas
City
St. Louis
25
The supplies, demands, and transportation costs per unit are shown on the network.
10
35
Demands
Transcribed Image Text:(a) Develop a linear programming model for this problem; be sure to define the variables in your model.
Let
X11 amount shipped from Jefferson City to Des Moines
X12 = amount shipped from Jefferson City to Kansas City
X13 amount shipped from Jefferson City to St. Louis
X21 amount shipped from Omaha to Des Moines
X22 amount shipped from Omaha to Kansas City
X23= amount shipped from Omaha to St. Louis
Min
s.t.
X11
X11
X11 +
+
X12
X12
X11 12 13 X21 X221 X23 20
X12 +
+
X13
X13
X13
x21
X21
X₂1 +
+
+
√x22 +
X22
X22
+
X23
X23
X23
Ś
Ś
=
=
=
(b) Solve the linear program to determine the optimal solution.
Jefferson City-Des Moines
Jefferson City-Kansas City
Jefferson City-St. Louis
Omaha-Des Moines
Omaha-Kansas City
Omaha-St. Louis
Total
Amount
Cost
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