Published electronically June 5, 2013

DOI:

10.1137/13S012509M3 Challenge Introduction**Authors: **Jenny Lai, Abram Sanderson, Amy Xiong, Lynn Zhang, and Roy Zhao (Wayzata High School, Plymouth, MN)

**Sponsor: **Thomas Kilkelly (Wayzata High School, Plymouth, MN)

**Summary: **The increased usage of plastic, paper, and other recyclable materials, due to convenience and efficiency, has not been matched by available recycling methods. These readily disposable goods have replaced reusable products such as glassware, resulting in landfills inundated by wastes—such as plastic and Styrofoam—that are not biodegradable (Rogers). While the immense consumption of plastics is harsh on the environment, these synthetic polymers are too integrated in modern-day society to be suspended or discontinued. How might we reconcile the use of these goods with cost-efficient recycling methods for every state and township in the United States?

Our team has been asked to predict the production rate of plastic waste over time, and to forecast the amount of plastic waste present in landfills in ten years. To begin, we assumed that while an increase in population over the next ten years will increase plastic waste output, and that there is a limit on the total amount of plastic generated that is discarded. Thus our model for production rate of plastic is sigmoidal in nature, with a carrying capacity (maximum amount of plastic discarded) of 30,000 tons/year. By integrating our sigmoid function, we predicted the amount of plastic waste present in landfills in 2023 to be 1,026,000 tons.

We were also asked to design a mathematical model that could determine which recycling method is most appropriate for a city, and apply it to Fargo, ND; Price, UT; and Wichita, KS. Our approach began with the assumptions that geographic location has a negligible impact on recycling rate for each method of recycling; each city will have at least one recycling facility; the use by citizens of drop-off and curbside pickup recycling is mutually exclusive; people will recycle in the correct manner; every household has recyclable wastes; and cities may be modeled as circles. Thus our first model considered the probability that a person would recycle at a drop-off center based on distance to the center. Our second model then determined the costs of collecting and operating curbside pickup, taking into account area, population density, and total household units of each city. Analysis led to the conclusion that Price, UT should employ drop-off recycling only, while Fargo, ND and Wichita, KS should employ curbside pickup as the most cost-efficient methods. On a national scale, we must report to the EPA how our model can lead to a municipal recycling guideline policy to govern all states and townships in the United States in an effort to mitigate the problem of recyclables not being recycled. Our model is best applied to cities and townships, as the factors considered—population, area, and household density—are specified on a city and township level. Furthermore, our model should not be used on a state level as states include cities and townships of varying sizes and development, including rural and urban regions. We conducted a cost-benefit analysis of each recycling method based on city population and area. Based on our analysis, we determined that it is more cost-efficient for cities with relatively small populations to adopt drop-off recycling only, while cities with larger populations to adopt curbside pickup recycling. Therefore we recommend that the EPA allows each municipality to determine their own recycling method based on our mathematical model because the variables involved in costs of recycling are unique to each municipality. However, as a general standard, the EPA should require all cities and townships beginning in 2016 to recycle by the method best for them, in order to put recyclables in their place so that future generations are not left to deal with a world wasted away.