A feasible solution is any choice of decision variables that satisfies all the given constraints of a linear programming problem, whereas an optimal solution is the single feasible solution or set of feasible solutions that achieves the best possible value for the objective function.

Yes, a feasible solution can easily exist without being optimal because any valid option that obeys every rule counts as feasible, but only the option that yields the maximum profit or minimum cost qualifies as optimal.

Yes. A feasible solution satisfies all the constraints and non-negativity requirements of the LP problem. An optimal solution is a feasible solution that gives the best possible objective value, such as maximum profit or minimum cost.

Yes, a feasible solution can exist without being optimal. There may be many feasible solutions, but only the one(s) achieving the best objective value are optimal.