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 show 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