Solving Linear Diet Model Problem: Step-by-Step Guide

In summary: He has gone over the solution multiple times and even had another calculus student check for errors, but cannot find a way to get a negative out of a natural logarithm. He has also tried using the absolute value of the log, but is unsure if this is the correct approach. Mitchell has shared his work in a PDF file and is seeking help in identifying any errors or misinterpretations. Thanks to the advice from Hurkyl and HallsofIvy, Mitchell has edited his solution and believes it is now more logical.
  • #1
mlowery
23
0
I am working on solving a linear diet problem. I am given a differential equation. The problem basically requires me to solve the D.E., then plug 'n chug. I have gone over the solution to the D.E. over and over again. A fellow calculus student has also looked over the math and cannot find the error. Quite possibly there is no error and I am misinterpretting something. I end up with a negative inside of a natural logarithm, but I cannot find a way to get it out. Additionally, I have tried simply using the absolute value of the log, but I don't think this is correct.

I have put the question along with my work into a PDF file located http://mlowery.t35.com/Special_Project_Weight_Loss.pdf"

If anyone could point out my error/misinterpretation, I would greatly appreciate it.

Thanks,
Mitchell
 
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  • #2
Why did you call k the initial weight? The initial weight is w(0). (Assuming the initial time is t = 0)
 
  • #3
Well my new answer seems more logical :)
Thank you so much Hurkyl.
 
  • #4
I presume you editted your answer based on what Hurkyl said. I solved the d.e. using a different method but got exactly the answer you did.
Good work!
 
  • #5
Yes, I did edit my answer based off of Hurkyl's advice. Thank you HallsofIvy for checking it as well.

Mitchell
 

1. What is a linear diet model problem?

A linear diet model problem is a mathematical optimization problem that involves finding the most cost-effective combination of food items that meets the daily nutritional requirements of an individual or a population. It is based on a linear programming approach, where the objective is to minimize the cost while satisfying constraints on the nutrient requirements.

2. Why is it important to solve linear diet model problems?

Solving linear diet model problems can help individuals and populations make informed and cost-effective food choices. It can also aid in addressing issues of malnutrition and food insecurity, especially in developing countries. Additionally, it can be used to optimize food supply for institutions such as hospitals and schools.

3. What are the steps involved in solving a linear diet model problem?

The steps involved in solving a linear diet model problem include defining the objective function, identifying the decision variables, formulating constraints based on nutritional requirements and food availability, solving the model using linear programming techniques, and interpreting the results to make food choices.

4. What are some challenges in solving linear diet model problems?

Some challenges in solving linear diet model problems include the complexity of real-world diets, limited availability or accuracy of data on food composition and prices, and varying nutritional requirements for different individuals or populations. There can also be challenges in interpreting the results and making practical food choices based on the optimized diet.

5. What are some potential applications of linear diet model problems?

Linear diet model problems have various potential applications, including developing personalized diet plans for individuals with specific health conditions, optimizing food choices for athletes or individuals with high nutritional needs, and planning food supply for schools, hospitals, and other institutions. It can also be used to assess the cost-effectiveness of different dietary interventions and policies.

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