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:
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.
- A pan measuring three meters in diameter
- 14,400 eggs
- 15 liters of oil
- 3 kilograms of butter
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?