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A. Nahsahpeemapetilon's paper "Historical antecedents for mythic figures within the Homeric narrative" has extensively documented a case that the inspiration for the monsters Scylla and Charybdis was in fact derived as covert caricatures of his in-laws, Patty and Selma Bouvier.
He further argues that the Sirens was based upon Homer's regard for a popular poet of the Springfieldian era, the bardic singer Lurleen Lumpkin.
The Burns Atom Smashing Plant was a dark place, and may have provided the basis for Homer's descriptions of the Underworld. Of particular note to this thesis is Charon's sycophantic relationship to Hades, who is depicted as greedy and ancient, while Charon's is obsequious with a barely concealed homosexual desire for his superior.
Easy: Donuts. And SpiderPigs.
It's a trick question. There are several Homers of that period: Homer of Springfield did not write the Iliad and the Odyssey, he wrote the Porkchopion. You should count yourself lucky to have a professor who wants to keep you on your toes.
Well, we know very little about the historical personage of Homer. Few things have come down to us, and even fewer are credible. However, let's look at some traditions about Homer:
He was blind.
He died upon being unable to answer the riddle "What we caught we threw away, and what we didn’t catch we kept".
Now, let's assess both of these within the context of his employment for Mr. Burns. First, why was he blind? Isn't it obvious? The radiation poisoning left him blinded after a mishap at the plant. Now, unfortunately, scholars have been wrong in their assessment of Homer. They have even based theories on how the Greeks saw color on his use of the word "wine-dark" to describe both the color of the sea and of oxen. I reject the theories that the Greeks had different ideas about color, or the more fringe theory that they saw different colors due to a vitamin deficiency. Instead, I posit that Homer saw different colors due to radiation poisoning.
Homer's riddle has been hotly debated by scholars for centuries. The traditional line of thought is that the answer is "fleas" or "lice." However, I reject the entire concept that Homer died after hitting his head while pondering a riddle. Instead, I take the riddle metaphorically, as a cautionary tale about properly rinsing when you have come into contact with radioactive particles. Homer failed to do this, and thus actually died of radiation poisoning.
Additional question; why did he name the Odyssey after that minivan they once rented? That thing had so many cup holders...
Dude, do your own homework. I bet you're the kind who marathoned the show three days before the deadline - the adulterated, semi-accurate version, mind. The real Homer was in fact a doughnut-eating, ale-drinking slob, but he had impeccable fashion sense. If you read Gumble (4.2ff), he has more than six passages berating Homer for his greed, but praising his "willingness to don, at every turn of the sun, clothes of the finest leather, silk and steel." [1]
Edit: Fine, okay, well, what do you think they all did there, and Burns and Smithers in particular? Lenny and Carl from that mockumentary (ha) were, of course, a stand-in for the wide acceptance of homosexuality in Homer's time. For more, see Bouvier, M., The All-American Family: The Invention of Penelope Simpson, Springfield Press, Ithaca (1992).
[1] Source: Gumble, B., The Lives of Bards, trans. A. Jackus, Springfield Press, Ithaca (1960).