Suppose we have a set of 3 products P = {1, 2, 3} and a set of 4 factory locations F = {1, 2, 3, 4}, where these products are manufactured. The products are transported from one factory to another at unit cost c_{i,j} with i,j ∈ F. Furthermore, each product has a price v_{p} with p ∈ P. Suppose also, that we transport x_{p,i,j} unities of product p from factory i to factory j with i,j ∈ F and p ∈ P. The data are as follows (Since x is 3dimensional,we use the notation x_{p=1} to “slice” (or extract) the matrix x_{i,j} where p = 1):


Using these data, we now can calculate various data using indexed notation (please verify as an exercise):
(1) The total transportation costs T is calculated as follows:
(2) The total value transported is as follows:
(3) The total transportation costs C_{p} for each product p ∈ P is:

(4) The value W_{i,j} transported between all factories (i,j) ∈ F × F is:

(5) The maximum quantity M_{i} transported from a factory i ∈ F is:

(6) For each product p ∈ P the sum of the maximum quantity S_{i} transported from a factory i ∈ F is:
