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Problem 6-02 (Algorithmic)

Consider the following network representation of a transportation problem:

The supplies, demands, and transportation costs per unit are shown on the network.

  1. 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 fill in the blank 1x11 + fill in the blank 2x12 + fill in the blank 3x13 + fill in the blank 4x21 + fill in the blank 5x22 + fill in the blank 6x23
    s.t.
    fill in the blank 7x11 + fill in the blank 8x12 + fill in the blank 9x13 = fill in the blank 10
    fill in the blank 11x21 + fill in the blank 12x22 + fill in the blank 13x23 = fill in the blank 14
    fill in the blank 15x11 + fill in the blank 16x21 = fill in the blank 17
    fill in the blank 18x12 + fill in the blank 19x22 = fill in the blank 20
    fill in the blank 21x13 + fill in the blank 22x23 = fill in the blank 23
    x11, x12, x13, x21, x22, x23 = 0
  2. Solve the linear program to determine the optimal solution. Enter “0” if your answer is zero.
    Quantity Cost
    Jefferson City – Des Moines fill in the blank 24 $ fill in the blank 25
    Jefferson City – Kansas City fill in the blank 26 fill in the blank 27
    Jefferson City – St. Louis fill in the blank 28 fill in the blank 29
    Omaha – Des Moines fill in the blank 30 fill in the blank 31
    Omaha – Kansas City fill in the blank 32 fill in the blank 33
    Omaha – St. Louis fill in the blank 34 fill in the blank 35
    Total Cost
    $ fill in the blank 36
 
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