Problem 6-02 (Algorithmic) Consider the following network representation of a transportation problem: Des Moines 225 126 270 Jefferson City 81 63 72 Kansas City 135 90 180 Omaha 45 St. Louis 90 1 1 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 node j. Min X11 + x12 + X131+ x21 + X22+ X23 s.t. X11 + X12 + X13 X21+ X221 + X2315 X11 X21 = X12 + X22 X13 X2315 X11, X12, X13, 21, 22, X23 20 b. Solve the linear program to determine the optimal solution. Enter "O" 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 $