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2. Healthy Choice (35 Points) A school dietitian wants to determine the best blend of meats to use in an order of 500 pounds of ground meat for hamburgers to be used for lunch at a local school. Three types of meat can be used in the blend with each having the following characteristics: Cost per pound % Fat % Protein % Water % Filler Meat 1 $0.75 15% 70% 12% 3% Meat 2 $0.8 10% 75% 10% 5% Meat 3 $0.98 4% 80% 8% 7% 7 The only requirement is that the blended meat consist of at least 75% protein and at most 10% each of water and filler. Although the dietitian wants to minimize his cost of filling the order, she would also like to provide a healthy lunch for the school. As a result, the owner also wants to minimize the fat content of the blended meat as well as cost. (a) State the decisions to be made, the objective and the constraints in words using = or = in the constraints. (Handwrite answer, 5 (b) Formulate this as a linear two objective algebraic optimization model. (c) Using Fat as objective 1 and Cost as objective 2, give an algebraic (d) Using your trade-off problem in (c), generate the Trade-off curve of (e) Identify the Efficient Frontier. (Hand in via Blackboard, 5 points) points) Carefully define your variables. (Handwrite answer, 5 points) formulation of the Trade-off Problem. (Handwrite answer, 5 points) Cost versus Fat using Excel. (Hand in via Blackboard, 5 points) 9 (f) What point on the Efficient Frontier Minimizes Fat? What is its corresponding Efficient Solution? (Hand in via Blackboard, 5 points) (g) What point on the Efficient Frontier minimizes Cost? What is its corresponding Efficient Solution? (Hand in via Blackboard, 5 points) 2. Healthy Choice (35 Points) A school dietitian wants to determine the best blend of meats to use in an order of 500 pounds of ground meat for hamburgers to be used for lunch at a local school. Three types of meat can be used in the blend with each having the following characteristics: Cost per pound % Fat % Protein % Water % Filler Meat 1 $0.75 15% 70% 12% 3% Meat 2 $0.8 10% 75% 10% 5% Meat 3 $0.98 4% 80% 8% 7% 7 The only requirement is that the blended meat consist of at least 75% protein and at most 10% each of water and filler. Although the dietitian wants to minimize his cost of filling the order, she would also like to provide a healthy lunch for the school. As a result, the owner also wants to minimize the fat content of the blended meat as well as cost. (a) State the decisions to be made, the objective and the constraints in words using = or = in the constraints. (Handwrite answer, 5 (b) Formulate this as a linear two objective algebraic optimization model. (c) Using Fat as objective 1 and Cost as objective 2, give an algebraic (d) Using your trade-off problem in (c), generate the Trade-off curve of (e) Identify the Efficient Frontier. (Hand in via Blackboard, 5 points) points) Carefully define your variables. (Handwrite answer, 5 points) formulation of the Trade-off Problem. (Handwrite answer, 5 points) Cost versus Fat using Excel. (Hand in via Blackboard, 5 points) 9 (f) What point on the Efficient Frontier Minimizes Fat? What is its corresponding Efficient Solution? (Hand in via Blackboard, 5 points) (g) What point on the Efficient Frontier minimizes Cost? What is its corresponding Efficient Solution? (Hand in via Blackboard, 5 points)