A cafe in New Orleans is selling three types of desserts: pralines, pecan pie and Bananas Foster! A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum. A pecan pie takes two cups of pecans, a cup of brown sugar, a cup of cane syrup, a cup of granulated sugar, a teaspoon of vanilla, and a tablespoon of rum. A recipe for Bananas Foster requires a cup of pecans, a cup of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum. Your pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum. Pralines sell for $22.68 per dozen, pecan pie costs $22.40 and Bananas Foster $15.

How many of each of these desserts should the cafe make in order to maximize their profits assuming they can only use the ingredients which they have on hand?