Problem 6-02 (Algorithmic) Consider the following network representation of a transportation problem: Des Moines 75 42 90 Jefferson City 27 21 24 Kansas City 45 30 60 Omaha 15 St. Louis 30 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. If constant is "1", it must be entered in the box. Let Xij = amount shipped from supply node i to demand nodej. Min X11 + X12 + X13+ X21+ X22+ X23 s.t. X11 + X12 + X13 X211 X22 + X2315 X11 X21 X12 X22 = X13 X23 X11, X12, X13, X21, X22, X23 20 b. Solve the linear program to determine the optimal solution. Enter "0" if your answer is zero. Quantity Cost Jefferson City - Des Moines $ Jefferson City - Kansas City Jefferson City - St. Louis Omaha - Des Moines Omaha - Kansas City Omaha St. Louis Total Cost