Linear Programing and the diet problem 

the diet problem is an operational research problem that encompasses various conditions (selected by the researcher), that allow a linear programming model to be made. This allows for a graphical view of the solution and is a quantitative approach to a potentially complex problem.

The solution to this type of problem was found between 1930 - 1940, when the U.S. army was trying to find an optimal solution to feeding their field troops while maintaining a healthy diet. One of the first solutions proposed was by a man called George Stigler. Years later, using hand operated computers and a team of 9 clerks, it was found that George Stigler's guess was only $0.24 cents off.

The breakdown of a problem like this requires all the necessary components of the problem to be organized  into different groups;

1. Sets - eg. like sets of food and sets of nutrients 

2. Parameters - eg. minimum and maximum prices / nutrients

3. Variables - eg.  number of servings of food

4. Objective function - eg. minimize the total cost of food 

5. Constrain Sets - eg. for each nutrient 'j' belonging to the set N, at least meet the minimum required level.

After the necessary components have been obtained and organized, the data is formatted for a computer model and then solved. 

Interpreting the results is up to the researcher and any modifications that need to made are done, which allows for a better models to be made after each revision.