Comparing multiple price options for many customer

Question

We have 1,000,000 customers. The cost of goods sold for each of them can be expressed as price A or price B.

Price A << Price B.

Price A and Price B are not linear to each other. In some cases B is 2 times as expensive, in some it is 100 times.

cost of all the customers on A is

min( (sum(A)/count(A)) , 100 ) * count(A) Effectively, the average cost of all the customers on A will be rounded up to 100 if it is less than 100.

There is no such restriction on B.

I would like to spend the least amount of money on their goods.

How do I maximize

cost=min( (sum(A)/count(A)) , 100 ) * count(A) + sum(B) I keep seeing this as a form of a dual knapsack problem, but I can't get it right ...

I'd be probably solving this in Python, most likely, although I doubt that matters much.

I've done manual analyses by assigning scores to x y z and filtering based upon that, I'm interested in more of a computational solution.

Any approaches to recommend?

Answer 1

Restated in a much easier way elsewhere.

Searching for the best fit price for multiple customers