Analysis of the Statement and Assumptions

The statement is an advertisement: "Buy pure and natural honey of company X." An assumption is considered implicit if the advertiser takes it for granted while making the statement. We must evaluate each assumption based on this.

I. Artificial honey can be prepared.

The advertisement emphasizes the qualities "pure and natural". This would be a pointless distinction if all honey was inherently pure and natural. By highlighting these words, the advertiser assumes that the consumer is aware of an alternative, such as impure or artificial honey, and that "pure and natural" is a desirable quality to seek out.
Verdict: This assumption is implicit.

II. People do not mind paying more for pure and natural honey.

The ad assumes that people value pure honey, but it makes no claim or assumption about its price. The honey from company X could be expensive, affordable, or cheap. The statement does not rely on the consumer's willingness to pay a premium.
Verdict: This assumption is not implicit.

III. No other company supplies pure honey.

This is an extreme conclusion. An advertisement exists within a competitive market. The ad's purpose is to persuade customers to choose company X's product over others, not to claim that it is the only one of its kind. It doesn't assume a monopoly on pure honey.
Verdict: This assumption is not implicit.

Conclusion

Only Assumption I is necessary for the statement to make sense as an advertisement.