The Professor is clearly a physicist and inventor. Is it ever shown why he is running a small scale shipping company with only a handful of employees, instead of (for example) working in a government lab or university research center?
For the money
Fry: This is awesome! Are we gonna fly through space fighting monsters and teaching alien women to lurve?
Farnsworth: If by that you mean "transporting cargo" then yes. It's a little home business I started to fund my research.
You may wish to note that the Professor does maintain an office at Mars University, something of a sinecure given that no-one ever takes his classes.
Farnsworth: No, I need it shipped to my office at Mars University. It's a little experiment that may well win me the Nobel Prize.
Leela: In what field?
Farnsworth: I don't care, they all pay the same.
Fry: Oh, I don't know. Hey, Professor, what are you teaching this semester?
Farnsworth: Same thing I teach every semester: The Mathematics of Quantum Neutrino Fields. I made up the title so that no student would dare take it.
Professor Farnsworth may have started the company to fund his research (see Valorums answer), but he also sees it as cheap source of labor for his projects (similar to a research group in a lab):
Farnsworth: This is not a business. I always thought of it more as a cheap source of labor, like a family.
from Future Stock