Published electronically July 22, 2014

DOI:

10.1137/14S013123M3 Challenge Introduction**Authors: **Anne Lee, Irwin Li, Steven Liao, Zack Polizzi, and Jennifer Wu (NC School of Science and Mathematics, Durham, NC)

**Sponsor: **Daniel Teague (NC School of Science and Mathematics, Durham, NC)

**Abstract**: Along with educating children on proper nutrition, schools are also responsible for providing healthy daily lunches to students. Eating properly has been shown not only to improve health but also to enhance classroom performance and reduce incidences of disease. Recent legislative acts such as the Healthy, Hunger-Free Kids Act of 2010 have been instrumental in pushing schools to offer more nutritious menu options. However, there have been many obstacles in the implementation and success of the program. Students have shied away from new school lunches, arguing that the healthier options are not as tasty. School districts also struggle to cover the rising expense of more nutritious foods with stretched budgets.

Our job is to develop a mathematical model to optimize the affordability, taste, and nutrition of school meals. The first step in this process is to develop a method to calculate the calories a student needs at lunch. Current calorie calculators give recommended values for an entire day while our method returns a result that can be specified to lunchtime needs based on attributes such as amount of sleep, whether or not breakfast is eaten, time spent exercising in the morning and afternoon, when you eat lunch and dinner, frequency of snacking, and weight. Based on these parameters, we are able to calculate a person’s rate of calorie burn throughout various periods of a day and find the amount of calories they

would need to consume at lunchtime.

We then sought to determine what percentage of high school students are satisfied by standard school lunches given the calorie requirements calculated in the previous step. We ran our model on data from a sample of 11,458 high school students across the country in order to determine the distribution of lunchtime calorie needs. Given that a standard school lunch contains 850 calories, we then calculated the frequency at which the student’s caloric needs fell in a fixed range of values above or below 850 calories. We found that currently, only 37.9% of students would be satisfied. By analyzing the distribution our model returned, we found that a 1,050 calorie meal was a more optimum solution that would satisfy a greater number of students (49%).

Finally, we established an ideal lunch meal for schools to offer to students based upon the recommendations of USDA’s MyPlate and what we observed to be the optimal number of calories to consume in order to satisfy the maximum percentage of students. Using data on foods available to a school and survey results showing how well students accept various foods, we were able to create an algorithm that generates meals that meet the USDA MyPlate requirement, have the necessary number of calories, and fit the available school budget. We then ranked these meals based on student acceptance to find the best meal choices, which would be well received by students while still meeting dietary and budget requirements. Using localized survey results allows our model to be customized for schools in different geographical and socioeconomic situations.