How will the right answer fit in terms of support and conclusion?

Only the right answer will add support for the conclusion.

Highlight the main conclusion in the passage, if there is one:

One should only buy a frying pan that has a manufacturer’s warranty

[CONCLUSION]. [SUPPORT].

So the argument totally changes the subject. It says you should get a warranty, because that shows manufacturers won’t “need to reimburse many customers”. The author didn’t even attempt to explain what reimbursing customers has to do with which pan you “should” buy, so that’s probably what the right answer will do.

Map the wording of the answers to the wording of the passage:

(A) Most people who buy a frying pan with a manufacturer’s warranty would seek reimbursement…

There’s the connection you’re looking for. If it’s true, manufacturers would really be paying out a lot on crappy pans. If companies want to avoid paying out, then the warranty really is an indication that a pan is higher quality. And now the author’s conclusion makes a lot more sense.

(B) …work at least as well at the time of purchase as any…

Does knowing pans with warranties work “at least as well” as pans without warranties really convince you that you “should only buy” one with a warranty? Wouldn’t you want to hear that it probably works better? This doesn’t add support for the conclusion, especially because it doesn’t address what the author meant by their statement about “the need to reimburse many customers”.

(C) The more a frying pan costs, the more likely it is…

The cost of the pan isn’t actually mentioned anywhere, only “paying more” for one with a warranty. So if you’re making a connection between this info and support for the conclusion, you’re probably adding in an assumption about why “costs” are relevant. You’re not supposed to do that.

(D) The most expensive frying pans…

…aren’t mentioned. More info about this specific group of pans doesn’t directly connect to the conclusion’s recommendation to “only buy a frying pan that has a manufacturer’s warranty”.

(E) …provide for full customer satisfaction.

This is the classic wrong answer that makes some sense in a real-world way, but doesn’t map to the author’s argument at all. It’s bringing in “customer satisfaction”, which the author never mentions directly. And it completely ignores the author’s assumption that the “need to reimburse many customers” has anything to do with whether you “should only buy” a pan with a warranty.

(A) is the correct answer.