Two managers both said their task comes first. Who gets to choose my afternoon?

At 11:20, the product manager asked me to finish a demo by four. Ten minutes later, my support manager sent a list of customer tickets and wrote, “These need you today.”

I’m shared between the two teams. Either task would take most of the afternoon. When I showed each manager the other request, both said theirs was the priority. The product manager suggested I “just get the urgent tickets out of the way.” The support manager said the demo could use yesterday’s version.

I can see why they disagree. The demo has a visitor coming specifically to see it; two of the tickets involve customers waiting for an answer I promised yesterday. I’m tempted to do a little of everything so nobody hears a flat no, but that could leave both pieces unfinished.

How would you handle the next message? I need a decision before lunch, and I don’t want to spend the afternoon pretending that two separate promises amount to one workable plan.