Teaser 2499: [Supermarket milk]
From The Sunday Times, 15th August 2010 [link] [link]
Joe was talking to the supermarket manager about shelf stocking, and she mentioned a recent exercise with milk. Each morning, they added sufficient new stock to ensure there were 1,200 litres on the shelves. They found that 56% of the new stock was sold on the first day, half that amount the next day and half that new amount the day after. Any remaining stock was regarded as out of date and removed next morning before restocking. Hence, they calculated the number of litres to be added each morning.
What is that number?
This puzzle was originally published with no title.
[teaser2499]
Hugh+Casement and 
S2T2 
Jim Randell 9:23 am on 16 June 2022 Permalink |
I assumed that the numbers are fixed. So the same quantity of fresh milk is added each day, and the same quantities sold each day.
If x litres of fresh milk are stocked at the beginning of the day (to bring the total stocks to 1200 litres).
We can track what happens to this batch milk on the following days.
At the start of the next day 0.56x has been sold, so there is only 0.44x of this batch of milk remaining (and a new batch of x litres of fresh milk are added).
At the start of the next day an additional 0.28x has been sold, so there is only 0.16x of the original batch remaining (along with 0.44x litres of the previous days new batch, and x litres of fresh milk).
At the start of the next day an additional 0.14x has been sold, so there is only 0.02x of the original batch remaining, but this is removed as it is too old.
So the 1200 litres of milk on the shelves consists of:
Hence:
Solution: Each morning 750 litres of fresh milk are added to the shelves.
So the milk available at the start of the day consists of:
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Hugh+Casement 8:55 am on 17 June 2022 Permalink |
That’s some supermarket! How ever many metres of shelf space do 1200 litres take up?
I suggest that a more realistic puzzle would have all the numbers a fifteenth as much.
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