A cyclic engine interacts with three thermal reservoirs in one cycle as follows: it absorbs 150 J of energy as heat from a reservoir at 600 K, absorbs 50 J as heat from a reservoir at 300 K, rejects 180 J of energy as heat to a reservoir at 400 K, and delivers 20 J of work. Using numerical entropy calculations, evaluate whether this cycle can occur, and justify your conclusion in no more than three sentences.