One summer when I was in college I worked as an intern for a spinoff company started by a professor, developing a new technology. I had worked for this professor on the same idea while it was still a research project at the University.
Over the course of several months it became evident to me that some serious issues of feasibility had not been thought through, or, sometimes, even considered, and that in my judgment the technology was going to require a lot more work and was much less likely to ultimately function correctly than the professor believed. I also perceived what appeared to be resistance on the part of the professor to considering these issues, but I am not always a good judge of personality so this may have been an illusion.
On the one hand, I felt that my role as an intern was to work on the professor's ideas as he envisioned them, so I should subordinate my own fears about feasibility and do what I could within the role I had. My judgment was, after all, just my judgment, and could have been wrong. On the other hand, it was the investors paying my wages and I did not feel right wasting their money on an idea that wouldn't ultimately pay off.
So I think my questions are:
(Also, as I suspect this may not be quite the right site for this kind of question, does someone know a more appropriate one?)
I'm not sure whether the project doesn't really have enough feasibility or you are unable to properly visualize the big picture. I doubt investor would invest money without thinking about feasibility and most likely even the professor would have thought about it.
In any case, IMO once you've joined a company as an intern, you shouldn't worry too much about feasibility. What would be better is that talk to your senior(s) and convey your thoughts specifying why according to you, is the project having some serious issues of feasibility and possibly suggest what can be done. (This is what even I did during my internship at a startup whenever I doubted feasibility of something.) Most likely you can expect some good response or otherwise if they hadn't really thought about it, they'll consider your opinions.
Not at all doubting your capabilities, but IMHO an intern is generally not in position to say whether his responsibilities assigned by the company are in conflict with the interest of the company. Communication with people around you is the key.
I usually have 2 or 3 interns on staff at my company who work on real problems and real projects. From my position as their director (professor) I tend to openly discuss many of the details about how it will be used and the end 'feasibility' of the products. And it's my style to always suggest and recommend they express any concerns, questions or ways it can be improved. My interns are smart, that's why I hired them and I don't expect them to be business experts but I would be perfectly find with them asking 'how are you going to sell this' or 'who the heck would use this?'
And I think if your professor didn't have a good answer to your questions then your thoughts of it's feasibility would be correct. He also shouldn't take offense to the question, and if he does then there is probably an issue.
But, interns are people too :] and they didn't hire you because you are dumb. Those candidates didn't get the gig.
The Investors are nothing to do with you, period.
(Excepting things like criminal actions wher you would obviously have a duty to disclose to authorities) However if your working relationship with the professor was such that you didn't think you could openly discuss the things he was asking you to work on then either
a) The Prof was unrealistic and had an inflated idea/opinion - in which case do you really want to work there?
b) You have the above faults. In which case you need a long hard look in a mirror.