题目236：美食篮
本帖最后由 欧拉计划 于 2017-1-6 02:03 编辑Luxury Hampers
Suppliers 'A' and 'B' provided the following numbers of products for the luxury hamper market:
Product 'A' 'B'
Beluga Caviar 5248 640
Christmas Cake 1312 1888
Gammon Joint 2624 3776
Vintage Port 5760 3776 Champagne Truffles 3936 5664
Although the suppliers try very hard to ship their goods in perfect condition, there is inevitably some spoilage - i.e. products gone bad.
The suppliers compare their performance using two types of statistic:
[*]The five per-product spoilage rates for each supplier are equal to the number of products gone bad divided by the number of products supplied, for each of the five products in turn.
[*]The overall spoilage rate for each supplier is equal to the total number of products gone bad divided by the total number of products provided by that supplier.
To their surprise, the suppliers found that each of the five per-product spoilage rates was worse (higher) for 'B' than for 'A' by the same factor (ratio of spoilage rates), m>1; and yet, paradoxically, the overall spoilage rate was worse for 'A' than for 'B', also by a factor of m.
There are thirty-five m>1 for which this surprising result could have occurred, the smallest of which is 1476/1475.
What's the largest possible value of m?
Give your answer as a fraction reduced to its lowest terms, in the form u/v.
题目：
供应商 'A' 和 'B' 提供下列数量的产品给美食篮市场：
产品 'A' 'B'
鲟鱼鱼子酱 5248 640
圣诞节蛋糕 1312 1888
腊肉 2624 3776
葡萄酒 5760 3776
香槟巧克力 3936 5664
尽管供应商们十分努力地装运他们的合格产品，但产品不可避免地会有损耗，比如说产品变质。
供应商们通过下面两种数据来比较他们的表现：
[*]每个供应商的五个单产品损耗率——即每种产品的变质数除以相应的产品供应数。
[*]每个供应商的总产品损耗率——即总变质产品数除以总产品供应数。
让他们惊讶的是，供应商们发现对于五个单产品损耗率，'B' 均高于 'A' 并为 'A' 的 m 倍，m>1； 而且，自相矛盾似的,对于总产品损耗率，'A'，均高于 'B'，并同样为 'B' 的 m 倍。
存在 35 个 m>1 使得上面的情况发生，其中最小的一个是 1476/1475。
m 最大的可能值是多少？
给出你的答案并化简，形式为 u/v。
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