With the patience of its customers and with its network strained to the breaking point, the on-line service company announced a series of new initiatives trying to relieve the congestion that has led to at least four class-action lawsuits and thousands of complaints from frustrated customers.



(A) the patience of its customers and with its network strained to the breaking point, the on-line service company announced a series of new initiatives trying to relieve

The use of “with” is redundant.

“strained to the breaking point” would refer only to network and not the patience of its customers- incorrect. 

What does “trying” modify? Initiatives or the on-line service company?

Incorrect.


(B) the patience of its customers and its network strained to the breaking point, the on-line service company announced a series of new initiatives that try to relieve

The sentence could also mean- the patience (subject) of X (customers)  and Y (network). To avoid such a meaning ambiguity, it is preferred to construct the sentence in such a manner that there is no scope for ambiguity.

- With its network (X) and the patience of.. (Y)- Now, the meaning is clear as in option C. 

The on-line service company announced a series of new initiatives that try to relieve- changes the meaning of the sentence. 

The company has announced a series of new initiatives (why? To try to relieve the congestion.. as in option C)


(C) its network and the patience of its customers strained to the breaking point, the on-line service company announced a series of new initiatives to try to relieve

Correct. 


(D) its network and with the patience of its customers strained to the breaking point, the on-line service company announced a series of initiatives to try relieving

The infinitive form is to be used because it shows an intent- to try to relieve. Eliminate 


(E) its network and its customers’ patience strained to the breaking point, the on-line service company announced a series of new initiatives to try relieving

Same as D. Eliminate