A Saturday Morning Optimization Problem

Published by MrHonner on

I recently faced an interesting optimization problem.

Through my local grocery store’s rewards program, I earned a one-time 20% discount, to be applied to a single future shopping trip.  Naturally I wanted to maximize the value of my discount, and the more I spent, the more I would save.  But like all optimization problems, there were a number of constraints involved.

shopping bags


First, I wanted to buy only things I would actually use.  This prevented me from buying things like saffron (expensive things that would drive up the value of my 20% discount) because I wouldn’t use them.  It also limited the quantity of high-priced proteins I would buy, as such things need to be consumed quickly to be enjoyed.

Second, I could only buy what I could carry, since I walk to and from the grocery store.  This put global constraints on the volume and weight of my purchases, which made me think about maximizing cost per-unit-weight/volume at a local level.

All in all, I’d say I did pretty well!  With some planning and foresight, the total value of my 20% discount ended up being around $46.  And I don’t think I’ll need to buy dried basil any time soon.

shopping receipt



    Fung · March 1, 2015 at 12:04 pm

    I don’t know much about saffron, but I do know that ice cream makes everything better!

Joshua Greene · March 2, 2015 at 2:51 am

This reminds me of another classic optimization problem: choosing what to eat at an all-you-can-eat buffet. Depending on the eater, variables involved include:
(1) cost of food if purchased elsewhere
(2) food preferences
(3) calories
(4) volume

Amanda · March 24, 2015 at 2:30 pm

And now I am wondering- If the 20% discount was $46.07, what was the original total for all of the groceries?

Shecky R · November 18, 2018 at 5:34 am

You should’ve bought enough additional chocolate to raise the savings over $50.

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