# Consider the following network representation of a transportation problem. Des Moines 25 15 45…

Consider the following network representation of a transportation problem. Des Moines 25 15 45 Jefferson City 9 8 Kansas City 20 8 11 20 Omaha 24 St. Louis 20 Supplies Demands 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 *11 = amount shipped from Jefferson City to Des Moines * 12 = amount shipped from Jefferson City to Kansas City X13 = amount shipped from Jefferson City to St. Louis X 21 = amount shipped from Omaha to Des Moines X22 = amount shipped from Omaha to Kansas City X23 = amount shipped from Omaha to St. Louis 14 * *11 + 9 Min s.t. X12 + 7 * *13 + 8 X21 + 10 X X22 + X X23 X11 + X12 + X13 X < 30 < 20 X22 X23 ? X21 X21 X 11 ? = 25 15 X 12 Xz2 = X X13 X23 = 10 X 11, 12, 13, 21, 22, 23 20 (b) Solve the linear program to determine the optimal solution. Amount Cost Jefferson City-Des Moines 5 14 X Jefferson City-Kansas City 15 x 9 x Jefferson City-St. Louis 10 X 7 Omaha-Des Moines 20 8 x Omaha-Kansas City Omaha-St. Louis Total 435 X

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