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## The Mathematics of Weight Loss

Research has shown that the Weight Watchers program tends to have more success than other programs. For example, in a 2003 study (Journal of the AMA), nearly 40% of the participants on the Weight Watchers program lost more than 5% of their body weight, which is double the success values of a comparison group trying to lose weight on their own.

Weight Watcher's magical formula is

where p = WW Points, c = Calories, f = Fat (grams), and r = Fiber (grams). The amount of WW points each dieter should have daily is based on their body weight, and how much weight they are trying to lose.

Sample these food values:

Medium Fries: c = 450, f = 22, r = 5
Quarter Pounder with cheese: c = 430, f = 30, r = 2
Cheeseburger: c = 330, f = 14, r = 2
Big Mac: c = 590, f = 34, r = 3
Corn on the Cob: c = 140, f = 2, r = 2
Low-fat Grilled Chicken Pasta: c = 873, f = 8.9, r = 10.3
Low-fat Asian Chicken Salad: c = 714, f = 9, r = 9.6
Low-fat Brownie Sundae: c = 326, f = 3.2, r = 4.6

Problem 1: Calculate the points for each of the above foods. Is it fair to just rank these foods by their points?

Problem 2: Try to create graphs (4-d is best?) to illustrate the equation...if nothing else fix r = 4 and build a 3-d model. What does it tell you (i.e. more than "The higher the fat and calories content, the more points in that food...but the higher the fiber, the less points.)

Small Note: Why does the equation use min{r,4} rather than just r?

Source: G. Trieu's "How many Weight Watchers Points is that?" Healthy Weight Forum, 7/18/2007