How do you use the words 'For Which' in an English sentence?

Question

I am trying to learn about on which, at which, on which, etc"

But I'm stuck with "for which" mostly 

 A. The shaded region to the right of the break-even point represents quantities for which the company makes a profit. 

B. The shaded region to the right of the break-even point which represents quantities for the company makes a profit.

Is sentence B same as sentence A?

2nd example of for which:

A. the luncheon for which we bought the food will take place outside.

B. the luncheon which we bought the food for will take place outside. 

Is sentence B same as sentence A and are they both grammatically correct?

Thank you,

Answer 1

"For which" is a more formal way of writing "which... for".

Whether you use "at which," "on which," or "for which" just depends on which preposition works best for your sentence. The preposition "for" generally describes the use, purpose, or duration of something.

So, in your second example, why was the food bought? It was bought for the purpose of eating at the luncheon. So use "for which." Now, let's compare:

A. The luncheon [for which we bought the food] will take place outside.

B. The luncheon, [which we bought the food for], will take place outside. 

The words in bold represent a complete, independent clause. This can stand alone as its own sentence. The words in [brackets] represent the dependent clause, which is what you're rearranging when you use "for which" instead of "which... for." Both sentence A and B mean the same thing and are technically correct in syntax, but sentence A is constructed more formally than sentence B.

Your first example is a little more tricky. In this context, "for" is being used to describe a duration or interval; in this case, the interval of quantities that will make the company a profit. A more simple sentence with this use of "for" might be something like, "He worked at the store for five years." Or, "For questions 1-5, I got the same answer."

So, in the first example, the company makes a profit for the interval represented by the shaded region. You could use "at which" here if you wanted to refer to a specific quantity, but "for which" works better because you are describing a range of quantities.

However, in the first example, the two sentences are not the same. Sentence B is grammatically incorrect because "which" is in the wrong place; it should come after the verb "represents." In this context, the word "which" is used a little differently; instead of introducing an unnecessary dependent clause, it describes "quantities" (the object of the sentence).

So, to make both sentences mean the same thing:

A.  The shaded region to the right of the break-even point represents [quantities for which the company makes a profit]. 

B. The shaded region to the right of the break-even point represents [which quantities the company makes a profit for].

We can ignore the crossed-out portion right now. Here, the portion in [brackets] represents the object clause, which answers the question, "what does the shaded region represent?" This is what you're rearranging when you use "for which" instead of "which...for". Leave the main verb where it is!

Answer 2

For which = which... for

We don't use this in everyday speaking as it is a more formal writing technique. Mentally you can think of the word "which" as the word "that".

For which is an expression used generally to explain the use of something or to explain the purpose of something