2010 HiMCM A题特等奖学生论文下载2543
2010 HiMCM A题特等奖学生论文下载2543
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论文摘要如下：
High School Mathematical Contest in Modeling 2010
Problem A: Bicycle Club
Summary
Based on existing bike stations in Chicago, Denver and Des Moines, our group aims to develop an efficient bike rental program and determine the locations in which new bike stations should be constructed. We first determined the factors that would impact bike usage. By categorizing existing bike stations according to zip codes, we found a general positive relationship between the number of bike stations and each of the various factors we studied, such as population density, civic center popularity, and the number of tourist attractions in within the zip code. After deriving and combining the functions, we were able to arrive at a final rating system: R = 3.1964e3.6396C + T + (3.926285282 * 10-5)(1.0000709285)P + 0.00141 0.0067125S
This rating system considers the relative weightings of each variable, and can be used to evaluate the need for new biking stations at certain locations.
To locate the different sites for upcoming bike stations that would efficiently serve the increase in bike usage and demand, we substituted data in our model to obtain ratings of the zip codes near city center. By comparing these different rankings and considering the maximum number of stations an area can carry, we found the ideal locations for the expansion of the bike program in the next five years in zip codes: 60611, 60605, 60616, 50309, 50312, 80204, 80205, 80206, 80209, 80210, 80211, 80218, 80223, and 80207.
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