Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins, Alan uses 1 third cup of oil and 2 eggs. For a tray of bran muffins, Alan uses 1 half cup of oil and 1 egg. Alan has 4 cups of oil and 12 eggs on hand. He sells trays of blueberry muffins for 12 dollars each and trays of bran muffins for 9 dollars each. Alan wants to maximize the money raised at the bake sale. Let x represent the number of trays of blueberry muffins and y represent the number of trays of bran muffins Alan bakes. What are the constraints for the problem?