Consider the following network representation of a transportation problem. Des Moines 20 15 50 Jefferson City 9 Kansas 10 City 10 40 Omaha 25 St. Louis 60 Demands 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. Let *11 = amount shipped from Jefferson City to Des Moines *12 = amount shipped from Jefferson City to Kansas City *13 = 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 X21 + 10 X27 + 25 X23 Min 15 X1 1 + 9 *12 + 8 X13 + s.t. 30 X 11 X 12 X13 20 X 21 X22 + X 23 25 X 21 X11 15 X72 X12 10 X13 X23St. Louis 60 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 *13 = amount shipped from Jefferson City to St. Louis *21 = amount shipped from Omaha to Des Moines *22 = amount shipped from Omaha to Kansas City X23 = amount shipped from Omaha to St. Louis Min 15 X 1 1 + 9 X 12 + 8 X 13 8 X21 + 10 X27 + 25 X 23 s.t. X11 X 12 X13 $ 30 X21 X 27 X23