Classic New Orleans desserts include pralines, pecan pie, and Bananas Foster — all three are absolutely essential to eat on any trip to the city. Chefs may quibble about this ingredient list as there are dozens of variations on each recipe, but these ingredients are common to most formulations. 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 and makes two servings. Bananas Foster is considered a dessert for two and is priced accordingly at $15. 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 and a pecan pie costs $22.40. The Sensitivity Report from an Excel formulation of this problem is shown below. What is your optimal solution (in order of X, Y, Z, max)

Variable Cells
			Final	Reduced	Objective	Allowable	Allowable
	Cell	Name	Value	Cost	Coefficient	Increase	Decrease
	$C$20	X	20	0	22.68	22.12	0.28
	$D$20	Y	0	0	22.4	0.28	7.4
	$E$20	Z	0	-7.4	15	7.4	1E+30
Constraints
			Final	Shadow	Constraint	Allowable	Allowable
	Cell	Name	Value	Price	R.H. Side	Increase	Decrease
	$G$13	Pecans LHS	20	0	24	1E+30	4
	$G$14	Brown Suger LHS	40	0.28	40	0	4
	$G$15	Cane Syrup LHS	0	0	12	1E+30	12
	$G$16	White Suger LHS	20	22.12	20	1.333333333	0
	$G$17	Vanilla LHS	10	0	40	1E+30	30
	$G$18	Bananas LHS	0	0	12	1E+30	12
	$G$19	Rum LHS	20	0	64	1E+30	44