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Re: [Help-glpk] Stigler's 1939 diet problem

From: Brady Hunsaker
Subject: Re: [Help-glpk] Stigler's 1939 diet problem
Date: Fri, 09 Nov 2007 11:08:20 -0500
User-agent: Icedove (X11/20061220)

Andrew Makhorin wrote:
Another example was added to glpk examples subdirectory, which is the
original Stigler's 1939 diet problem (please see the model below).

I am wondering (if there is a dietologist on the list :) why in dietary
problems one requires nutrients to be *not less* than recommeneded
allowance while it would be more resonable to require them to be *equal*

I am not a dietician, but I regularly use a diet problem as a project for undergraduates learning linear programming. They collect actual data from fast-food restaurants. I think that you're correct that a good diet would have values close to the recommended values for each nutrient--not just greater than.

I think the reason that Stigler used greater than is that each of the nutrients on his list are ones for which the usual problem is not getting enough. It's rare that anyone has too much vitamin A in their diet, for example.

For other "nutrients" like total fat or sodium, however, a less than constraint would generally make more sense.

When I assign the problem, I use a different set of "nutrients", and I let the students decide whether to use a greater than constraint, less than constraint, or double bounded constraint. It's good practice for them to think about which makes sense in advance, but then also to react to the solution they get by reconsidering their choices.

The one exception is that I require that they satisfy the calorie constraint exactly.


Brady Hunsaker
Assistant Professor
Industrial Engineering
University of Pittsburgh

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