May one write something like: "We shall need many snarks to this end. However, they can be fed carrots and the latter are cheap this year. Which makes me hope..."?
Your sentence, when put on the page, would typically be punctuated as follows, with the relative clause not starting a new (typographic) sentence :
...the latter are cheap this year, which makes me hope...
... the latter are cheap this year—which makes me hope...
The antecedent of which in this case is not a particular noun but the nominal idea expressed in the preceding statement(s), and so the which-clause is tacked onto the preceding sentence, so to speak, adding new information rather than modifying a previous word or phrase.
An alternative would be:
... the latter are cheap this year, and this makes me hope...
where this again refers back to the idea expressed in the preceding clause(s) rather than to a particular word or phrase.