Problem 6-02 (Algorithmic) Consider the following network representation of a transportation problem: Des Moines 500 280 600 Jefferson City 180 140 160 Kansas City 300 200 400 Omaha 100 St. Louis 200 1 Supplies Demands The supplies, demands, transportation costs per 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 X X111 X X121+ X X13+ 16 X X21+ 20 X X221+ 10 X X23 s.t. 1 X11+ 1 X12 + 1 X13 60 X 1 X21 + 1 X22+ 1 X23 40 x 1 X11 1 X21 50 x 1 x12 1 X22 30 X 1 X13 1 X23 20 x b. Solve the linear program to determine the optimal solution. Enter "0" if your answer is zero. Cost Quantity 10 x Jefferson City - Des Moines $ 280 X Jefferson City - Kansas City 30 x 540 X Jefferson City - St. Louis 20 x 280 X Omaha - Des Moines 40 X 640 X Omaha - Kansas City 40 X 640 X Omaha - St. Louis 0 o Total Cost $ 1,760 X