Mathematical Model of a Transportation Problem

where

m number of sources

n number of destinations

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

bj demand of j-th destination (in tons, pounds, liters, etc.)
cij 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.)
xij amount of material shipped between i-th source and j-th destination (in tons, pounds, liters etc.)