矿产资源合理利用是保障国家经济可持续发展的基本要求，如何有效利用矿产资源是经济问题也是管理问题。本文首先以矿产资源开发利用的最优化为目标，以微分方程和泛函变分的方法相结合，考虑储量、价格、采掘率、开采成本等要素，构建了一个泛函最大值模型来量化，从而用矿产资源开采模型确定不可再生矿产资源的最优采掘率的方案，即在矿产市场价格不低于一个与时间相关的函数值时，用最大开采率开采，否则停止开采。接着文章讨论了建立数学模型对矿产资源问题进行量化分析的局限性，阐述了运用数学方法解决矿产资源问题的思考，提出了矿产资源问题与数学方法相结合的有关建议。%The rational utilization of mineral resources is a fundamental requirement to guarantee the sustainable economic development of our country ,how to utilize mineral resources effectively is a problem in both the aspects of economy and management .In this paper ,we firstly put the optimization of exploiting and using mineral resources as the target ,combined differential equation with calculus of variation ,and took reserves ,prices ,exploiting rate and cost of mining into consideration to build a model of maximum of function for quantification in order to formulate the optimalscheme of exploiting rate:If the price of ore market is higher than a function value that related with time ,we should exploit it with the maximum exploiting amount ,otherwise stop mining .Next we discussed the limitation of building mathematical model to analyze the problems of mineral resources ,expounded thinking of using mathematical method to solve these problems ,and put forward advices of combining problems with themethod .
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