LPP

The initial solution of a transportation problem is said to be non-degenerate basic feasible solution if it satisfies:
→The solution must be feasible, i.e. it must satisfy all the supply and demand constraints.
→The number of positive allocations must be equal to m+n-1, where m is the number of rows and n is the number of columns.
→All the positive allocations must be in independent positions
A few terms used in connection with transportation models are defined below.
1. Feasible solution: A feasible solution to a transportation problem is a set of non-negative allocations, xij that satisfies the rim (row and column) restrictions.
2. Basic feasible solution: A feasible solution to a transportation problem is said to be a basic feasible solution if it contains no more than m + n – 1 non – negative allocations, where m is the number of rows and n is the number of columns of the transportation problem.
3. Optimal solution: A feasible solution (not necessarily basic) that minimizes (maximizes) the transportation cost (profit) is called an optimal solution.
4. Non-degenerate basic feasible solution: A basic feasible solution to a (m x n) transportation problem is said to be non – degenerate if, the total number of non-negative allocations is exactly m + n – 1 (i.e., number of independent constraint equations), and these m + n – 1 allocations are in independent positions.
5. Degenerate basic feasible solution: A basic feasible solution in which the total number of non-negative allocations is less than m + n – 1 is called degenerate basic feasible solution.
Note: It is very standard and regular question and asked in UGC-NET Dec-2015 paper-3
Ref-https://solutionsadda.in/ugc-net-cs-2015-dec-paper-3/