Is the following problem NP-Hard?
(I have posted this answer as a comment on the question, but I am reposting it with a little more detail.)

This problem is NP-hard as follows.

As is usual in a proof of NP-hardness, suppose that a natural number K is also given as part of input, and consider the yes/no problem of deciding whether at least K customers are satisfied.  Then this problem is NP-complete, even if it is restricted to the case where X=1, m=3K and each customer wants to buy exactly three goods.  (Note that if X=1, the value of Y is irrelevant as long as Y&gt;0.)  In this case, the problem is equivalent to the NP-complete problem called Exact Cover by 3-Sets.

See Garey and Johnson for more on complexity theory and NP-completeness, including the definition of the Exact Cover by 3-Sets and the proof of its NP-completeness.