Beyond the immediate problem of availability of cash for its day-to-day operations, the economic viability of the company depends on
its ability for improving its efficiency and capturing the market through innovative products.
A. its ability for improving its efficiency and capturing-> Improving and capturing are parallel. and, "its" refer can to company. Let's re-read it, company's ability for improving company's efficiency and capturing. It doesn't make sense.
B. whether it can improve its efficiency and capture-> Improve and capture are parallel. and, "it/its" refer can to company. Let's re-read it, company can improve company's efficiency and capture. It is better. Let's keep it. Note- In idiom "whether on not", "or not" is often not used. It is correct here.
C. if it can improve its efficiency and capture-> "if" is incorrect to use. To use "if" we need future tense further.
D. whether or not it has the ability to improve its efficiency and can capture-> "to improve" and "can capture" are not parallel.
E. the ability for it to improve its efficiency and capture->Let's re-read it. the economic viability of the company depends on the ability for company to improve....Doesn't make sense.
So, I think B.