A chef working at a MR. Eggs franchise is preparing Mr. Eggs’ famous giant breakfast omelets. These omelets requires not only the finest grade AA eggs, but also at least two of the following specially prepared ingredients: tomatoes, diced ham, onions, mushrooms, cheese and shrimp. These ingredients are measured in cups. When the chef cooks an omelet, she must follow Mr. Eggs’ strict recipes:
She can never use onions and mushrooms in the same omelet.
For every cup of diced ham, she must also use a cup of mushrooms, but if mushrooms are used, she does not have to use diced ham.
If cheese is included in the omelet, the number of cups she uses must be greater than the total number of cups she uses for all the other specially prepared ingredients combined in that omelet.
For every cup of tomatoes used, she must use two cups of onions.
No omelet uses all of the specially prepared ingredients.
She cannot use any ingredients other than the ones listed above.