Consider the following network representation of a transportation problem. Des Moines 30 15 35 Jefferson City 9 8 Kansas City 15 10 30 Omaha 23 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 = 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 1x 2 + |x 2 + |x 3 + x1 + x2 + 0*23 | | s.t. X11 + X12 + X13 + X22 + X21 X21 X23 X11 + VIVI X12 + X22 *13 + X23 *11* *124*13, 21, 2223 20 (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 Consider the following network representation of a transportation problem. Des Moines 30 15 35 Jefferson City 9 8 Kansas City 15 10 30 Omaha 23 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 = 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 1x 2 + |x 2 + |x 3 + x1 + x2 + 0*23 | | s.t. X11 + X12 + X13 + X22 + X21 X21 X23 X11 + VIVI X12 + X22 *13 + X23 *11* *124*13, 21, 2223 20 (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