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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Topic Video
Question
Please help with part D
![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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e1761aa-60ba-4e50-b21a-206672dc0a7b%2Fc5bf1d78-db35-42ae-a306-9ef7464fe3e9%2Fiktznad_processed.png&w=3840&q=75)
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?
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)