Consider the following network representation of a transportation problem.LetMin40s.t.35SuppliesFrom Jefferson CityFrom OmahaTo Des MoinesJeffersonCityTo Kansas CityOmahaTo St. Louis1498X11= amount shipped from Jefferson City to Des MoinesX12= amount shipped from Jefferson City to Kansas CityX13= amount shipped from Jefferson City to St. LouisX21 amount shipped from Omaha to Des MoinesX22= amount shipped from Omaha to Kansas CityX23= amount shipped from Omaha to St. Louis81124The 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.Des MoinesKansasCitySt. Louis251040Demands (b) Solve the linear program to determine the optimal solution.Jefferson City-Des MoinesJefferson City-Kansas CityJefferson City-St. LouisOmaha-Des MoinesOmaha-Kansas CityOmaha-St. LouisTotalAmountINADOCost

Decision Variables: Suppose-X11 = amount shipped from Jefferson City to Des MoinesX13 = amount…

Consider the following network representation of a transportation problem. Let Min 40 s.t. 35 Supplies From Jefferson City From Omaha To Des Moines Jefferson City To Kansas City Omaha To St. Louis 14 9 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 = amount shipped from Omaha to St. Louis X23 8 8 11 ☐☐☐☐☐ 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 24 Des Moines Kansas City St. Louis 25 10 40 Demands

Consider the following network representation of a transportation problem. Let Min 40 s.t. 35 Supplies From Jefferson City From Omaha To Des Moines Jefferson City To Kansas City Omaha To St. Louis 14 9 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 = amount shipped from Omaha to St. Louis X23 8 8 11 ☐☐☐☐☐ 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 24 Des Moines Kansas City St. Louis 25 10 40 Demands

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 93P: This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits...

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This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.
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