**Feasible solution:**when non negative values of x_{ij }where i= 1 , 2 , …m and j= 1 , 2 , …n satisfy the constraints of availability or supply and demand or requirement is called the feasible solution of the transportation problem.**Basic feasible solution:**it is that feasible solution that contains only m + n -1 non-negative distribution.**Optimal solution:**when the transportation cost is minimum then the feasible solution is said to be the optimal solution.**Balanced transportation problem:**a transportation problem in which the total supply from all the sources equals the total demand in all the destinations.

Mathematically, _{i=1} ʃ^{m }a_{i} = _{j=1}ʃ^{n} b_{i}

**Unbalanced transportation problem:**such problems which are not balanced are called unbalanced.

Mathematically, _{i=1}ʃ^{m }a_{i ≠ j=1}ʃ^{n} b_{i}

**Matrix terminology:**transportation problem is also solved by the matrix system. As we all know in matrix the vertical cells are called columns and horizontal cells as rows.

Warehouse

1 2 3 4

Plants A 4 2 10 3

B 6 8 7 8

Demand 15 7 8 12

The intersecting point that is row B and column 4 also written as (B, 4) is the unit cost 5.