i received a private message about this thread.

the difference between (d) and (e) this problem is, in my opinion, not dispositive; in this particular problem, a case could be made for either of those choices. therefore, if you eliminated the first three choices (presumably by using parallelism), you are pretty much where you want to be with this one.

in general, the modifier "to + verb" is used to signal the goal or purpose of an action/statement, while "for + verbing" conveys the idea that the action is, in some generic way, oriented toward the process of "verbing".
in many instances, therefore, both constructions are fine. for instance:
i need to get a new pair of shoes to run --> this sentence implies that "to run" is the ultimate goal (which, presumably, hasn't yet been achieved). in other words, according to this wording, i can't run until i get a new pair of shoes; therefore, "to run" is the ultimate goal or purpose of getting a new pair of shoes.
i need to get a new pair of shoes for running --> this sentence just means that i need to get a new pair of running shoes (= shoes whose purpose is oriented toward the general process of running). this sentence is different, in the sense that it doesn't portray the act of running some sort of remote goal or purpose that hasn't yet been achieved; it merely identifies the reason why i'm getting the shoes.

here's a pair of examples that is a little more like the sentence here:
our company needs to create a new position to manage shipments --> here, "to manage shipments" is a remote goal that has not yet been achieved; in other words, our company probably doesn't even have a shipping and receiving department yet. therefore, we need to establish a new position with that ultimate goal.
our company needs to create a new position for managing shipments --> here, "managing shipments" is just stated as a general purpose; it's probably something that our company already does, but, for some reason, it has now become incumbent upon us to create a separate department for it.