From a Calvinist perspective, does Limited Atonement make the Gospel offer empty?

It seems to me that the limited atonement of Calvinism makes the Gospel offer seem empty. Let's say that I hear someone saying that he is in need of $100 and I tell him "I have $100, I can give it to you if you want", and he replies "That's ok, one of my friends already told me that he'd help me out", and when he leaves the room I tell the other guys that were present there "I told him I'd give him the money, but I don't actually have $100" ... what would you think of my character? Would that show that I'm a man of integrity? Not at all. That's how I think God would be if the limited atonement point of Calvinism is true. The Gospel is offered to everyone, right? God commands all people from everywhere to repent and believe the Gospel, correct (Mark 1:15, Acts 17:30)? Why would God extend His gift of salvation to everyone who believes (John 3:16) if that offer is empty for some? **How do Calvinists explain this?**