How to chose a store by optimizing my costs? Let's say that I wanted to chose between two grocery stores (store $a$ and store $b$) in my area. They have the same items, and they both charge a variable price / cost for each product ($a_1$, $b_1$, $a_2$, $b_2$ for $n$ products). I don't know how often I'll need to buy any particular item, I just know that I will need to buy food in general (have to eat!). How can I make sure that I choose the right store to optimize / minimize my total cost? 
First, how would I properly describe this type of problem? What are some possible ways of approaching this? Are there certain statistical models that are better suited for this type of problem? (Be it traditional regression models, Bayesian models, machine learning, etc). I want to learn more but having trouble finding good information (likely due to my inability to properly describe what I'm looking for). 
From comments:
Let's assume there is a known probability that I will have to buy each item on any given trip ($p_1, p_2, \dots, p_n$).  
 A: Your situation is actually rather straightforward.  You simply want to compare two weighted sums.  On a typical shopping trip, you will purchase each item with probability $p_{i}$ and cost $c_{ij}$, where $i$ indexes the items and $j = \{a, b\}$ indexes the stores.  Thus the expected cost for each item is $p_ic_{ij}$.  You simply calculate those values for each item and sum them up for each store.  That is your long run expected total cost for a shopping trip to each store.  You compare the two weighted sums to find which is lower.  You would prefer the store with the lower weighted sum, if you are obliged to shop at only one store.  
On the other hand, if you can switch between stores at will and you know what items you will need to purchase on a given trip, you can just add those prices for each store and go to the one that will give you the cheaper total price.  
Of course, if it is sufficiently convenient to go to both stores, you could go to the first store and buy all the items that are cheaper there, and then go to the other store to buy the rest. That way you would always pay the minimum price.  
