Because the cork stoppers in wine bottles can leak

Clearly, the second boldface sentence is the conclusion made in the argument. There is nothing to debate about it.
Answering this question would be relatively easy if you focus on the use of “only slightly higher” in the first boldface sentence. “Only slightly higher” adds positively to the conclusion made in the argument. If it were just “higher” or “somewhat higher” then it would have opposed to conclusion. So, bold face statement here, in light of other information provided, supports the claim. Hence, B is the answer.

Understanding the passage:

Defects of cork stoppers often cause a lot of wastage of wine. New plastic stoppers by Bottlemaster Inc. is superior to the cork stoppers and devoid of these defects. Yet they are made available at only a slightly higher price. Meanwhile, cork stoppers are expected to be more expensive soon. This makes us believe that BM's plastic stoppers will grab more of the market share for wine stoppers.

Conclusion:Bottlemaster's plastic stopper will increase its share of the market for wine-bottle stoppers.

Prethinking:

BF1: Bottlemaster's plastic stopper is available to winemakers for a price only slightly higher than that of traditional cork stoppers
This information by itself is strictly not in support of the conclusion since it states that plastic stoppers are more expensive. But together with the other premises in the passage, we can see that the plastic stoppers offer much more cost-benefits. Hence it supports the conclusion.

BF2: Bottlemaster's plastic stopper will increase its share of the market for wine-bottle stoppers.
This is the main conclusion. it is supported by BF1.

Option Analysis

A) The first and the second each provide evidence to support the conclusion of the argument.
The first does provide evidence in support of the conclusion, but the second is the conclusion itself. Therefore this is an incorrect option.

B) The first presents information that, in light of other information presented, provides evidence to support the conclusion of the argument; the second is that conclusion.
This option is in line with our prethinking. Hence this is the correct answer.

C)The first is evidence that has been used to support a position that the argument opposes; the second is the conclusion of the argument.
The first can be called an evidence to support a position; but that position /standpoint is the main conclusion itself. It does not oppose the argument. This part is incorrect. The second is indeed the conclusion.

D)The first is evidence that has been used to support a position that the argument opposes; the second provides evidence to support the conclusion of the argument.
The first statement is the same as option C, which is incorrect. The second part is incorrect since BF2 is the conclusion and not an evidence to support the conclusion.

E) The first is a claim that the argument challenges; the second is a conclusion on which that challenge is based.
The first is not a claim that is challenged. It is a fact used to support the argument. The second is indeed a conclusion. But there is no such challenge as mentioned.

The first claim is evidence for a plastic stopper after stating the issues of a wood cork, the second is the conclusion and outcome.

A addresses is only half right. The second phrase does not provide evidence.

C, and D are wrong because there is no supporting a position in the argument in the previous phrases. We've only seen the argument mention the current wood cork issues, and failures up to this point.

E is wrong because there is no challenge, and the conclusion does not challenge wood corks. The conclusion only states why plastic would be a better alternative than wood.

B is correct since it follows the issues of a wood cork with the benefits, and costs of a plastic stopper.