In calc when teaching the 'min surface area of a can with given vol, of which soln is diameter = ht, I wrote a cat foot company telling them how much they'd save by making their cans taller. Got a letter from the marketing dept telling me a million reasons for the can's design.
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As others have said, if you still have it, please share the letter. I'd love to use it the next time I teach Calc I.
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so...were they correct?
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My letter to the cat-food company was more in jest. I realized there are many reasons for the size of a can of cat food other than the 'optimal surface area size.' I was interested in how they would respond. I think they had a lot of fun answering my query.
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it looks like they had fun. I'm impressed with their answer—though I'd have no idea if it were true or they just made it up!
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No, I'm sure their responses were based on fact and that they weren't just making stuff up.
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You probably made some engineer’s day when marketing fwd’d that email (letter?) asking for input. “I’ve been waiting 20 years for this question” as he rolls up his sleeves...
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That doesn't read like it's from marketing. That reads like an exasperated engineer having to explain to yet another person without full understanding of the design parameters why the product is the way it is.
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I bet that letter caused some poor engineer some serious pain when some executive came to him, letter in hand, and asked why the hell they were pissing away company money on excess material.
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Don't be silly, packaging technical experts barely ever to complete that many sentences in a row before someone runs away, that person was thrilled
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OK, Tim, we need a container that is durable, easy to open, lightweight, can withstand temperatures high enough to heat treat the product inside, is food safe, and space efficient. Oh, and marketing wants it to be a purple pyramid.
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Reality has often more parameters than you can imagine...
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This needs to be a case study in a product design/packaging class.
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Good they have a reason as solid as yours
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This is great but cans of human food have all the same constraints yet are much closer to the minimum surface area. What’s different about cat food? Is it just that the end user tries to shove their whole face into the can?
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I think this is the first time I've seen a business 'win' a debate with these smart-alec letters!
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The textbook we currently use (Stewart) has an extended exercise that addresses points 4 and (more-or-less) 2, but not the others. The conclusion is that optimal sizes vary from h=d to tall and thin, which completely fails to account for tuna cans.
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apparently h<d are easy to sterilise, just like h>d ones. Somehow h=d ones occupy their own set of awkwardness. Alternatively, that's bollocks, like the "it takes too long to switch both height and diameter when processing" (what, like tuna cans?)
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That's probably right, though why sterilisation cost should be the dominant factor I don't know. Presumably a can with an inverse h/d ratio would do as well for sterilisation, but it would be impossible to empty.
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That’s a bold cat food can response
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