自然数分拆与最佳基金计划——2001年全国大学生数学建模竞赛C题

Natural Number Distribution and the Best Bonus Plan --2001 Mathematical Contest in Modeling Problem C

文章运用路径分解的思想方法 ,依照不同的投资途径以分解资金流向 (定理 1) ,建立起一套严密的投资组合与奖金发放的数学理论 ,它适用于任意n年基金计划的制定 .此文的关键之处 ,在于找到了“历经k年的、本息增长最迅速的投资路径” ,并发现它只与k的自然数分拆有关 .对问题 1得到相应的最佳分拆构造的mod 5周期性 (定理 2 ) ;对问题 2又得到了最佳分拆构造的mod 6周期性 (定理 3) .精确求解出了 3个问题 :问题 1:基于分拆的mod 5周期性 ,所得最佳计划使得每年发放奖金约为 10 9816 9元 .问题 2 :基于分拆的mod 6周期性 ,最佳基金计划使每年发放的奖金约为 12 75 2 0 6元 .问题 3:最佳计划使得第 3年发放奖金 1498191元 ,其余各年发放 12 48492元 .

This article by using the routine broken down method, with different inventment ways for breaking down the fund flow(definition 1),establishes a strict inventment combination and bonus distribution mathematics theory, which is suitable for formulating any year fund plan. The key points of,this article lie in finding the most rapidly increasing interest of inventment routine,with K years and that it only has relationship with the matural number distribution of k: mode 1,obtaining the best distribution constitution of mod 5 cyclicity (definition2);mode 2,obtaining the best distribution constitution of mod 6 cyclicity(definition 3).Exactly working out 3 problems: Mode 1: with distribution of mod 5 cyclicity,obtaining the best plan of bonus distribution about 1 098 169 yuan every year. Mode 2: with distribution of mod 6 cyclicity,obtaining the best plan of bonus distritution about 1 275 206 yuan every year. Mode 3: with the best plan,the third year bonus distribution is 1 498 191 yuan,the remaining years being 1 248 492 yuan.