Official Explanation
Split #1: "every" vs. "every other". The Engineering Department is a department, and it can't have more extensive facilities than itself! The appropriate comparison is between this department and "every other" department. Choices (A) & (C) make this mistake.
Split #2: the "due to" mistake. The word "due" is an adjective, a noun modifier, so it must modify the noun it touches. The noun "every other department" is not "due to" anyone's demand for anything. We are trying to modify the action of the previous clause, and a noun modifier cannot perform this task. We need the verb modifier "because of." Choices (A) & (D) make this mistake.
Split #3: idiom with "demand". The idiom "P's demand for Q" means that P is the actor doing the demanding and Q is the thing demanded. Thus, "its graduates' demand for industry" in (C) would mean that the graduates were demanding industry—that's so wrong that it's not even clear what it would mean. Choice (C) is wrong.
The reverse construction in (A) & (E), "industry's demand for their graduates," gets the logic correct: yes, industry has a demand—industry is demanding the graduates.
An alternate way to express this is to say "its graduates' demand in industry," the version in (B) & (D). The construction "demand in" is not really an idiom by itself. It's just that the graduates experience a demand, and this demand is taking place in industry. This is a perfectly fine way to express this. Only (C) makes the idiom mistake.
Split #4: pronoun agreement. The "Engineering Department" may have many members, both faculty and students, but it's a singular collective noun, and we need to refer to it by a singular pronoun: "it". Choices (D) & (E) use the incorrect plural pronoun. In fact, (E) makes that mistake, and then it makes the double-whammy mistake of using the same pronoun, "their," to refer to two different antecedents back-to-back, first the "Engineering Department," then the "graduates. This is a second pronoun mistake: choice (E) is a train wreck in terms of pronoun rules.
Split #5: the correspondence. What corresponds to what? the graduates have a higher demand in industry and this corresponds to the higher salaries they receive. Higher corresponds to higher, so we need to modify the adjective "higher"—we need the adverb to modify the adjective: "correspondingly higher." Only choices (A) & (B) have this correct.
The only possible answer is (B).