The Difference between Finite Dimensional Linear Programming Problems and Infinite Dimensional Linear Programming Problems

This paper studies the difference between finite-dimensional linear programming problems and infinite dimensional linear programming problems. We discuss a special class of continuous linear programming problems. We develop the structure of extreme points of feasible region for this problem. Under some conditions we can characterize all extreme points of this problem. We show that under some conditions the optimal value for this problem may be finite but there is no optimal solution for it. Finally, we construct an example for this problem which has an optimal solution but all extreme points for this problem are not optimal solutions