Case Study Practice: Optimising Can Design and Quality Control | 案例分析实战：优化罐体设计与质量控制

📚 Case Study Practice: Optimising Can Design and Quality Control | 案例分析实战：优化罐体设计与质量控制

Case studies in CCEA Year 13 Mathematics challenge you to bring together pure mathematical techniques and statistical methods to solve real-world problems. This article guides you through a complete worked case study – from optimising the shape of a drinks can to monitoring the filling process with hypothesis tests. By following every step, you will see how calculus, algebra, probability and inferential statistics combine to support practical business decisions.

CCEA 13 年级数学的案例分析要求你将纯数学技巧与统计方法融合，以解决现实问题。本文带你一步步完成一个完整的实例演练——从优化饮料罐的形状，到用假设检验监控灌装过程。通过追踪每一步，你将看到微积分、代数、概率与推断统计如何共同为实际商业决策提供支持。

1. The Business Scenario | 商业情景

A soft drinks company produces cylindrical aluminium cans that must hold exactly 330 ml of liquid. The management team wants to minimise the amount of metal used per can to cut material costs, while ensuring every can meets the capacity requirement. Meanwhile, the quality control department regularly checks the filling process to see whether the average volume matches the declared 330 ml and whether the proportion of leaking cans remains within acceptable limits – currently set at no more than 5%.

一家软饮料公司生产必须精确容纳 330 毫升液体的圆柱形铝罐。管理层希望尽量减少每个罐子的金属

Published by TutorHao | Year 13 Mathematics Revision Series | aleveler.com

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