Question

Prove: Every extreme point of the convex set of feasible solution of the system Ax=b, xge0 corresponds to a BFS.

Answer 1

In linear programming, every extreme point of the convex set of feasible solutions of a system corresponds to a basic feasible solution (BFS).

Step-by-step explanation:

In linear programming, a basis is a subset of the variables that uniquely determines all the other variables. A basic feasible solution (BFS) is a feasible solution where exactly m of the variables are set to 0, and rest of them are determined by the basis variables. In a convex set of feasible solutions of the system Ax=b, x>=0, every extreme point corresponds to a BFS.