As envisioned by researchers, commercial farming of lobsters will enab

As envisioned by researchers, commercial farming of lobsters will enable fisheries to sell the shellfish year-round, taking advantage of off-season demand, standardize its sizes and colors, and to predict sales volume in advance.

"taking advantage of off-season demand" correctly modifies the act preceding the comma - "to sell". By selling the shellfish year-round the fisheries take advantage of off-season demand.

But, what follows after the modifier must be congruent with what "commercial fishing of lobsters" will enable fisheries to do:
(1) enable fisheries To sell....
(2) enable fisheries (to) standardise
(3) and enable fisheries to predict sales volume.

The non-underlined portion of the sentence really does dictate the structure here.

For the reasons above, B is correct and the below are incorrect
(A) taking advantage of off-season demand, standardize
Standardize is not logically consistent. Taken literally, A says "will enable fisheries standardise"

(C) taking advantage of off-season demand, standardizing
C is incorrect because the participle "standardizing" modifies either the act of selling year round or taking advantage - neither of which makes sense.

Back-to-back modification is typically incorrect unless one statement is essential and the other non-essential.

(D) take advantage of off-season demand, standardizing
Again, not consistent.

(E) take advantage of off-season demand, to standardize
turning "take" into a verb instead of leaving it an infinitive breaks the grammatical parallelism, but also makes this list non-sensical.

"enabled X to sell, take..., to....