Consider the following network representation of a transportation problem. 60 30 Jefferson City Omaha 15 59 co 00 24 Des Moines Kansas City St. Louis 25 20 45 Supplies The supplies, demands, and transportation costs per unit are shown on the network. (a) Develop a linear programming model for this problem; be sure to define the variables in your Let Demands
Consider the following network representation of a transportation problem. 60 30 Jefferson City Omaha 15 59 co 00 24 Des Moines Kansas City St. Louis 25 20 45 Supplies The supplies, demands, and transportation costs per unit are shown on the network. (a) Develop a linear programming model for this problem; be sure to define the variables in your Let Demands
Management, Loose-Leaf Version
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Author:Richard L. Daft
Publisher:Richard L. Daft
Chapter4: Managing In A Global Environment
Section: Chapter Questions
Problem 1SGB
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![Consider the following network representation of a transportation problem.
Let
60
Min
30
Jefferson
City
Omaha
15
9
8
8
11
24
Des Moines
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
+8x21 +11x22
15x11
+9x12 + 8x13
Kansas
City
St. Louis
Supplies
The supplies, demands, and transportation costs per unit are shown on the network.
(a) Develop a linear programming model for this problem; be sure to define the variables in your model.
+24x23
25
20
45
Demands](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F862c5bc2-e09a-4feb-bd28-f7638a835094%2F5fa70692-6a31-40de-a853-8e9dc66af708%2Fgg1vo3v_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following network representation of a transportation problem.
Let
60
Min
30
Jefferson
City
Omaha
15
9
8
8
11
24
Des Moines
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
+8x21 +11x22
15x11
+9x12 + 8x13
Kansas
City
St. Louis
Supplies
The supplies, demands, and transportation costs per unit are shown on the network.
(a) Develop a linear programming model for this problem; be sure to define the variables in your model.
+24x23
25
20
45
Demands
![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
15x11 + 9x12 +8x13 + 8x21 +11x22 +24x23
Min
s.t.
From Jefferson City *11+x12 +13 ≤ 60
From Omaha
To Des Moines
To Kansas City
To St. Louis
X21 +22+x23 ≤ 30
*11+x21 = 25
*12+x22
X11*12*131X211*221 Х23 2.0
(b) Solve the linear program to determine the optimal solution.
Amount
Cost
Jefferson City-Des Moines
Jefferson City-Kansas City
Jefferson City-St. Louis
Omaha-Des Moines
*13+x23=45
Omaha-Kansas City
Omaha-St. Louis
= 20
Total](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F862c5bc2-e09a-4feb-bd28-f7638a835094%2F5fa70692-6a31-40de-a853-8e9dc66af708%2Fglhi4wx_processed.png&w=3840&q=75)
Transcribed Image Text: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
15x11 + 9x12 +8x13 + 8x21 +11x22 +24x23
Min
s.t.
From Jefferson City *11+x12 +13 ≤ 60
From Omaha
To Des Moines
To Kansas City
To St. Louis
X21 +22+x23 ≤ 30
*11+x21 = 25
*12+x22
X11*12*131X211*221 Х23 2.0
(b) Solve the linear program to determine the optimal solution.
Amount
Cost
Jefferson City-Des Moines
Jefferson City-Kansas City
Jefferson City-St. Louis
Omaha-Des Moines
*13+x23=45
Omaha-Kansas City
Omaha-St. Louis
= 20
Total
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