。
Yumi got up early to listen to an English program.
Literal
Yumi [topic-は] English-of program [object-を] listen-[purpose-ために] early wake-up-[polite-past-ました].
~ために is the purpose construction: '[for the purpose of] X-ing.' Attaches to a verb's dictionary form. 早く is the adverbial form of 早い ('early, fast'). A perfectly clear sequence: purpose + time adverbial + main verb. 番組 ('program, broadcast') is common media vocabulary.