What's the use of double rules?

It is inferred that the objective function value corresponding to any feasible solution of 1 maximization problem is a lower bound of the optimal objective function value of its dual problem.

There is an upper limit to the maximization problem—

Inference 2 The objective function value corresponding to any feasible solution of minimization problem is an upper bound of the optimal objective function value of its dual problem.

Inference 3 If both the original problem and the dual problem have feasible solutions, they all have optimal solutions.

Inference 4 If the original problem (dual problem) is unbounded, its dual problem (original problem) has no solution. Its inverse does not hold.