We have been asked by management to spend a very short period of time to "size" a software project - that is, to give them a very loose ballpark of time to implement the entire thing.
There are three major components (backend, ios, android), each to be the responsibility of one developer with domain expertise. Each person has been given thirty minutes to come up with a number.
We have been given a one-page requirements document, have extrapolated some coarse user stories, and a coarse flow doc. We're developers, not project managers, and there is no Project Owner as our company is in pre-sales on this project and wants to give the prospective client a loose number.
As developers we are uncomfortable with giving numbers on such a limited foundation. During development we generally do Scrum (stories, points, sprints, standups, velocity, etc), so once we're working on a project our estimates come easily and have some basis in reality. In this case though, there is no project yet and we're unsure of how best to proceed.
How should we handle this? And in future, how could our company do things better?