The Mathematics of Hungry Cats


I haven’t felt like taking out a loan, renting a pick-up truck, building an annex to my home, and buying a two year supply of cat food for my two cats. Making just one stop for cat food every two years is an attractive plan, but it comes with unreasonable associated costs. On the other hand, I don’t mind stopping every two weeks. That’s not a mad hassle and it’s not a budget buster. Two cases every two weeks has seemed just fine, but inevitably, demand sneaks up on and exceeds supply, and then crisis mode kicks in. I hate making a special trip for cat food at 9:50 PM just so the wild animals won’t starve to death before I can make it to the cat store.

At first I thought I could use my Reminder app and figure out some 2-case/3-case pattern every so many weeks, but the repeat menu is limited. So then I wondered how I could most efficiently buy cat food once only every two weeks and still ensure that my cats will never be hungry again.

Google Spreadsheet killed this problem. Number rockets can fiddle with different amounts, explore different initial conditions (Do we need an initial condition?), and let their rules play out over several months until they are satisfied with their solution. Is it simple? Is it efficient? Is it easy for a harried human to operate?

QUESTION: Two cats each eat one can of cat food twice every day. Cat food is sold in cases of 24 cans. What is the most efficient way to buy cat food once only every two weeks (because that’s an easy schedule to remember) and always be sure to have enough cat food on hand?

Cat Food Spreadsheet is here

Cat Food Graph x-axis: #weeks. y-axis: #cases of cat food.

click for Desmos view