易拉罐的最优化问题

Optimization Problems of Cans

从一道导数应用题目出发,分析了当前市场上销量极大的饮料(如可口可乐、雪碧、健力宝等)的包装采用易拉罐的原因,综合应用了求导数,一元函数无条件极值,多元函数条件极值,Lagrange乘数法得出在同等容积下,当取高是直径的2.4倍时,所用材料最省的结论。

This article is a derivative application topic. It discussed the reason of the can m the packing drink （for example Coca - Cola, Sprite, Jianlibao and so on） , which have a big sale on current market. This topic has applied the derivative computation, a circular function extreme value, the function of many variables condition extreme value, the Lagrange multiplicator law. Considering the actual material used and ramming welding, it achieves the most superior conclusion that high is 2.4 time as diameter under the same level volume.