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