Mathematical Model of a Transportation Problem

where

m … number of sources

n … number of destinations

a_i … capacity of i-th source (in tons, pounds, liters, etc)

b_j … demand of j-th destination (in tons, pounds, liters, etc.)
c_ij … cost coefficients of material shipping (unit shipping cost) between i-th source and j-th destination (in $ or as a distance in kilometers, miles, etc.)
x_ij … amount of material shipped between i-th source and j-th destination (in tons, pounds, liters etc.)