Mark each of the below as either true or false with a brief (e.g., 1 sentence) explanation. (a) An optimal solution is always a BFS solution. (b) A BFS is the only optimal solution if none of its adjacent BFS solutions are better (as measured by the value of the objective function). (c) There always must be at least one optimal solution. (d) The number of BFS solutions can be infinite. (e) If a feasible solution is optimal but not a BFS then infinitely many optimal solutions exist.