A Saturday Morning Optimization Problem
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.
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.
5 Comments
Amy Hogan · March 1, 2015 at 9:32 am
A suggested use for saffron? http://www.grubstreet.com/2015/02/worlds-most-expensive-scoop-of-ice-cream.html
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.