Holiday Meal Turkey Ranch Presented by Olivia Ortega

Holiday Meal Turkey Ranch Presented by: Olivia Ortega Jen Kakacek Nikole Ellison

Holiday Meal Turkey Ranch n n The Holiday Meal Turkey Ranch is considering buying two different brands of turkey feed and blending them to provide a good, low-cost diet for its turkeys Let X 1 = number of pounds of brand 1 feed purchased X 2 = number of pounds of brand 2 feed purchased n n n n Minimize cost (in cents) = 2 X 1 + 3 X 2 subject to: 5 X 1 + 10 X 2 ≥ 90 ounces (ingredient constraint A) 4 X 1+ 3 X 2 ≥ 48 ounces (ingredient constraint B) 0. 5 X 1 ≥ 1. 5 ounces (ingredient constraint C) X 1≥ 0 (nonnegativity constraint) X 2 ≥ 0 (nonnegativity constraint)

Holiday Meal Turkey Ranch COMPOSITION OF EACH POUND OF FEED (OZ. ) INGREDIENT BRAND 1 FEED A 5 n Holiday Meal Turkey B 4 C Ranch data 0. 5 Cost per pound INGREDIENT 2 cents BRAND 2 FEED MINIMUM MONTHLY REQUIREMENT PER TURKEY (OZ. ) 10 90 3 48 0 3 cents 1. 5

Holiday Meal Turkey Ranch n n Using the corner point method First we construct the feasible solution region The optimal solution will lie at on of the corners as it would in a maximization problem – 20 – Pounds of Brand 2 n X 2 Ingredient C Constraint 15 – Feasible Region 10 – Ingredient B Constraint Ingredient A Constraint 5– 0 |– | 5 | | | 10 15 20 Pounds of Brand 1 | 25 X 1

Holiday Meal Turkey Ranch n n n n We solve for the values of the three corner points Point a is the intersection of ingredient constraints C and B 4 X 1 + 3 X 2 = 48 X 1 = 3 Substituting 3 in the first equation, we find X 2 = 12 Solving for point b with basic algebra we find X 1 = 8. 4 and X 2 = 4. 8 Solving for point c we find X 1 = 18 and X 2 = 0

Holiday Meal Turkey Ranch n Substituting these value back into the objective function we find Cost = 2 X 1 + 3 X 2 Cost at point a = 2(3) + 3(12) = 42 Cost at point b = 2(8. 4) + 3(4. 8) = 31. 2 Cost at point c = 2(18) + 3(0) = 36 n The lowest cost solution is to purchase 8. 4 pounds of brand 1 feed and 4. 8 pounds of brand 2 feed for a total cost of 31. 2 cents per turkey

Holiday Meal Turkey Ranch X 2 n Using the isocost approach Choosing an initial cost of 54 cents, it is clear improvement is possible Feasible Region 20 – Pounds of Brand 2 n – 15 – 54 Di re 10 – 31 . 2¢ 5– =2 X 1 ¢= cti on +3 2 X 1 of +3 X Iso 2 De co cr ea sin X os (X 1 = 8. 4, X 2 = 4. 8) | | 5 ine g. C 2 0 |– st L | t | 10 15 20 Pounds of Brand 1 | 25 X 1

Holiday Meal Turkey Ranch n Setting up Solver to solve the Holiday Meal Turkey Ranch problem

Holiday Meal Turkey Ranch Brand 1 Brand 2 Left Handside Right Hand Side Surplus Objective Function 2 3 0 Ingredient A 5 10 0 >= 90 Ingredient B 4 3 0 >= 48 -48 Ingredient C 0. 5 0 0 >= 1. 5 -1. 5 Solution Values 0 0

Holiday Meal Turkey Ranch n. Questions?