Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the following network representation of a transportation problem. 50 25 Supplies Jefferson City Omaha 15 9 8 8 11 25 Des Moines Kansas City St. Louis 30 15 30 Demands

Consider the following network representation of a transportation problem. 50 25 Supplies Jefferson City Omaha 15 9 8 8 11 25 Des Moines Kansas City St. Louis 30 15 30 Demands

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
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.
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.
 
From Jefferson City ??????
 
 
 
From Omaha ???????
 
 
 
To Des Moines ???????
 
 
 
To Kansas City ????????
 
 
 
To St. Louis ????????????
 
 
x11, x12, x13, x21, x22, x23 ≥ 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    
Omaha–Kansas City    
Omaha–St. Louis    
Total    
**Network Representation of a Transportation Problem** The diagram provided is a network representation of a transportation problem, showcasing how goods are transported from supply nodes to demand nodes. It includes two supply nodes—Jefferson City and Omaha—and three demand nodes—Des Moines, Kansas City, and St. Louis. **Supplies:** - Jefferson City: 50 units - Omaha: 25 units **Demands:** - Des Moines: 30 units - Kansas City: 15 units - St. Louis: 30 units **Transportation Costs:** - Jefferson City to Des Moines: 15 units cost - Jefferson City to Kansas City: 9 units cost - Jefferson City to St. Louis: 8 units cost - Omaha to Des Moines: 8 units cost - Omaha to Kansas City: 11 units cost - Omaha to St. Louis: 25 units cost **Explanation:** - The arrows represent the direction of goods flowing from the supply nodes (Jefferson City and Omaha) to the demand nodes (Des Moines, Kansas City, and St. Louis). - The numbers next to each arrow are the transportation costs for shipping goods between those nodes. - The supplies (50 units from Jefferson City and 25 units from Omaha) must meet the demands (30 units for Des Moines, 15 units for Kansas City, and 30 units for St. Louis) while minimizing the transportation costs. This model is essential for determining the most cost-efficient way to transport goods from suppliers to consumers, thereby optimizing the allocation of resources in the transportation network.
Transcribed Image Text:**Network Representation of a Transportation Problem** The diagram provided is a network representation of a transportation problem, showcasing how goods are transported from supply nodes to demand nodes. It includes two supply nodes—Jefferson City and Omaha—and three demand nodes—Des Moines, Kansas City, and St. Louis. **Supplies:** - Jefferson City: 50 units - Omaha: 25 units **Demands:** - Des Moines: 30 units - Kansas City: 15 units - St. Louis: 30 units **Transportation Costs:** - Jefferson City to Des Moines: 15 units cost - Jefferson City to Kansas City: 9 units cost - Jefferson City to St. Louis: 8 units cost - Omaha to Des Moines: 8 units cost - Omaha to Kansas City: 11 units cost - Omaha to St. Louis: 25 units cost **Explanation:** - The arrows represent the direction of goods flowing from the supply nodes (Jefferson City and Omaha) to the demand nodes (Des Moines, Kansas City, and St. Louis). - The numbers next to each arrow are the transportation costs for shipping goods between those nodes. - The supplies (50 units from Jefferson City and 25 units from Omaha) must meet the demands (30 units for Des Moines, 15 units for Kansas City, and 30 units for St. Louis) while minimizing the transportation costs. This model is essential for determining the most cost-efficient way to transport goods from suppliers to consumers, thereby optimizing the allocation of resources in the transportation network.
Expert Solution
steps

Step by step

Solved in 6 steps with 12 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS