I am pretty sure that the third of the following answers represented above is the option that correctly completes the sentence. Because we have the word ''company'' which is singular noun (so we can immediately omit the first option {corporations} and the last is the plural form {corporations}. Then the second option because it is simply spelled improper. So, what we have is corporation's with right usage of possessive 's'.
The sentence must look like that:
According to the corporation's policies, Staci is allowed to take the requested amount of vacation time.
