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A female bodybuilder is designing her diet leading up to a competition. To meet her macronutrient goals, she needs to consume at least 240 grams of protein and at least 30 grams of fat per day. Additionally, she needs to eat at most 120 grams of carbohydrates per day. Her goal is to meet these goals while minimizing her sodium intake. She plans to eat only three foods: eggs, white rice, and oatmeal. Each serving of eggs has 6 grams of protein, 5 grams of fat, and no carbohydrates. Each serving of white rice has 4 grams of protein, no fat, and 40 grams of carbohydrates. Finally, each serving of oatmeal has 6 grams of protein, 3 grams of fat, and 20 grams of carbohydrates. The eggs, white rice, and oatmeal has 60, 2, and 80 units of sodium respectively. (a) Define the decision variables. (b) What is the objective? Convert the objective to a maximization objective. (c) Give all constraints for this linear programming problem. (d) Give all constraints for this linear programming problem so that all inequalities are in < form.

A female bodybuilder is designing her diet leading up to a competition. To meet her macronutrient goals, she needs to consume at least 240 grams of protein and at least 30 grams of fat per day. Additionally, she needs to eat at most 120 grams of carbohydrates per day. Her goal is to meet these goals while minimizing her sodium intake. She plans to eat only three foods: eggs, white rice, and oatmeal. Each serving of eggs has 6 grams of protein, 5 grams of fat, and no carbohydrates. Each serving of white rice has 4 grams of protein, no fat, and 40 grams of carbohydrates. Finally, each serving of oatmeal has 6 grams of protein, 3 grams of fat, and 20 grams of carbohydrates. The eggs, white rice, and oatmeal has 60, 2, and 80 units of sodium respectively. (a) Define the decision variables. (b) What is the objective? Convert the objective to a maximization objective. (c) Give all constraints for this linear programming problem. (d) Give all constraints for this linear programming problem so that all inequalities are in < form.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.CT: Test
Problem 24CT
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Question 2 A female bodybuilder is designing her diet leading up to a competition. To meet her macronutrient goals, she needs to consume at least 240 grams of protein and at least 30 grams of fat per day. Additionally, she needs to eat at most 120 grams of carbohydrates per day. Her goal is to meet these goals while minimizing her sodium intake. She plans to eat only three foods: eggs, white rice, and oatmeal. Each serving of eggs has 6 grams of protein, 5 grams of fat, and no carbohydrates. Each serving of white rice has 4 grams of protein, no fat, and 40 grams of carbohydrates. Finally, each serving of oatmeal has 6 grams of protein, 3 grams of fat, and 20 grams of carbohydrates. The eggs, white rice, and oatmeal has 60, 2, and 80 units of sodium respectively. (a) Define the decision variables. (b) What is the objective? Convert the objective to a maximization objective. (c) Give all constraints for this linear programming problem. (d) Give all constraints for this linear programming problem so that all inequalities are in < form. (e) Convert the linear programming problem to a system of linear equations by introducing the appropriate slack variables and M. (f) Create the initial tableau and apply the Simplex Method. Be sure to give the particular solution of the final tableau. (g) How many servings of each type of food should the bodybuilder eat each day? What is the minimum amount of sodium consumed? (h) If she actually is only able to eat 90 grams of carbohydrates, what would be the new final tableau? What is the new optimal diet and how much sodium would be consumed?
Transcribed Image Text:Question 2 A female bodybuilder is designing her diet leading up to a competition. To meet her macronutrient goals, she needs to consume at least 240 grams of protein and at least 30 grams of fat per day. Additionally, she needs to eat at most 120 grams of carbohydrates per day. Her goal is to meet these goals while minimizing her sodium intake. She plans to eat only three foods: eggs, white rice, and oatmeal. Each serving of eggs has 6 grams of protein, 5 grams of fat, and no carbohydrates. Each serving of white rice has 4 grams of protein, no fat, and 40 grams of carbohydrates. Finally, each serving of oatmeal has 6 grams of protein, 3 grams of fat, and 20 grams of carbohydrates. The eggs, white rice, and oatmeal has 60, 2, and 80 units of sodium respectively. (a) Define the decision variables. (b) What is the objective? Convert the objective to a maximization objective. (c) Give all constraints for this linear programming problem. (d) Give all constraints for this linear programming problem so that all inequalities are in < form. (e) Convert the linear programming problem to a system of linear equations by introducing the appropriate slack variables and M. (f) Create the initial tableau and apply the Simplex Method. Be sure to give the particular solution of the final tableau. (g) How many servings of each type of food should the bodybuilder eat each day? What is the minimum amount of sodium consumed? (h) If she actually is only able to eat 90 grams of carbohydrates, what would be the new final tableau? What is the new optimal diet and how much sodium would be consumed?
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