Sid: I reply under the assumption that you are not a patent attorney; and the following are informational comments, not legal advice. Apologies if you think I am "talking down". Not intentional.
Concerning use, if I own a patent to something (a screw, a lamp, a new chemical, a widget, anything) anybody who uses or markets that patented something is an infringer.
You asked: "[my] question is: Can I buy these ingredients and combine them into a new product without infringement?" As I best understand your post, I analogize it to a bicycle with a battery powered light. If the bicycle and the light are each separately patented and you market a bicycle having a battery powered light, you would infringe both patents.
Having said that, depending on what each of the two patented items are marketed for and whether you buy from the patent owner (or authorized person), you might be be protected by a so-called "label license". If the situation is as cut-and-dried as your question suggets and you are already aware of the relevant patents, a competent IP attorney should be able to give you a concrete answer, based on the specific facts and without further patent searching, in about 1 or 2 hours time.