By installing special electric pumps, farmers’ houses could be heated

@noboru, this problem deals with advanced modifier where the initial phrase impacts not only the main subject but also the main verb of the sentence.
(A/B) >> Modifier Problem: "By installing special electric pumps" is modifying “houses” in A and “the warmth” in B;
(C/E) >> Grammatically, all of CE & D are correct. Meaning-wise also, both an engineer and a farmer can install a pump. But, we shall look for the meaning in the whole sentence which goes much beyond away from just the noun getting impacted by the initial phrase. This distinction actually makes this problem superior than other problems where the initial modifier just impacts the ensuing main subject noun.

In this problem, the ensuing main verb in the sentence is also getting impacted by the initial phrase.
The strategy to tackle such problems of modifiers where multiple subjects or similar subjects are fitting in the modifier schema is to check the applicability of the modifier to the entailing main verb in the sentence. Here, “installing” in modifier phrase has no bearing on “reports”(main verb) in CE, though has correct bearing on “could use”(main verb) in D.
Let us take example from the current problem.

If we restructure CE, we get “engineer reports(main verb) by installing pumps engineer(initial phrase)” which is wrong. Looking meaning-wise at D, we can say “farmers could use(main verb) warmth …. by installing pumps(initial phrase)”, which is correct.
(D) >> Correct