What I don't understand in the question is how "cool",which is an adjective,go parallel with past participle such as provided and milked.Please help

We continued this discussion via private message, but here's a summary for the benefit of others.

I agree, the generality of this statement is key. By using the future tense, (E) makes a prediction or statement of expectations.

I think the parallelism of (A) is still incorrect, and punctuation has something to do with it. Here's (A), with color-coding of what might be parallel:

For the farmer who takes care to keep them cool, providing them with high-energy feed, and milking them regularly, Holstein cows are producing an average of 2,275 gallons of milk each per year.

Note that "producing" cannot be parallel to the other -ing words!! "Providing" and "milking" act as modifiers, whereas "are producing" is a tensed verb. Also, if "producing" were in our list of three things, the "and" would be in front of the third item, not the second.

There's no -ing word before the first comma to parallel "providing" and "milking," so this is just a list of two things and there's no reason to have a comma in front of "and milking" at all.

Finally, even if we took the comma out, it doesn't make sense for "providing" and "milking" to be used as adverbial modifiers of "takes care to keep them cool." Providing food and milking them aren't ways to keep cows cool, unless there's something important about cow tending that I am unaware of (quite likely!). The structure of (A) could be OK, if we solved both the comma problem and the meaning problem:

For the farmer who takes care to keep them cool, providing them with adequate water and air-conditioning their shelters in the summer, Holstein cows are producing (better, as discussed above: will produce) an average of 2,275 gallons of milk each per year.