The Optimal Solution to a Standard Linear Programming Problem Need

Essay

The optimal solution to a standard linear programming problem need have no more non-zero-valued decision variables than there are linear constraints.The standard balanced transportation model, in which total supply equals total demand, has one linear constraint restricting the amount shipped from each of the m source nodes and one linear constraint restricting shipments into each of the n demand nodes.For this model, which is simply a special case of linear programming, the number of non-zero-valued decision variables in the optimal solution need be no more than one less than the total number of linear constraints.Why?