To my mind, the correct answer is “to help the reader understand how the fuel system on a spacecraft works to help the reader understand the difficult decisions faced by Mission Control”. The aim of including a problem-solution text structure is to organize the author´s ideas in a way that helps the audience to gain understanding of the text. In addition, this device is very useful to call the attention of the audience and to make the text more appealing to them.
The sentence in which the underlined infinitive phrase functions as a subject is the last one - to quickly move large groups of people is the purpose of public transportation.
<em>To quickly move </em>is the infinitive phrase, and it is a subject.
