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Eggs Anyone?

An epic French tradition is the preparation of giant omelettes. According to legend, the tradition began when chefs in the town of Bessières cooked a large omelet for Napolen during his travels through the south of France.

Now, every Easter Monday is focused on producing enormous omelettes in a small coastal town near St Tropez on the Cote d'Azur. It is considered to be a celebration by the town's local "omelette brotherhood."

The necessary ingredients for this venture:

  • A pan measuring three meters in diameter
  • 14,400 eggs
  • 15 liters of oil
  • 3 kilograms of butter
The giant omelet is stirred together by multiple chefs using giant wooden spoons. It is served to about 4000 people, along with giant loafs of fresh bread.

Once the breakfast is over, the festival participants (an option) compete in a 10 kilometer "fun run" to burn off those gained calories.

Question: I want to cook a 3-egg omelet. Assuming the ratios remain constant, what should be the diameter of the pan? How much oil and butter?