Final answer:
The sentence uses 'could' correctly to indicate that Tony and his wife had the opportunity to have breakfast together in the past.
Step-by-step explanation:
The use of the word 'could' in the sentence 'Tony and his wife woke up early so that they could have breakfast together before going to work.' implies that they had the ability or the opportunity to have breakfast together before work. This is different from 'shall' which is a future tense auxiliary verb used to indicate a strong likelihood or determination to do something in the future, while 'will' is used to express future intentions or promises. The sentence is correctly using the past tense modal verb 'could', which indicates that Tony and his wife had the option or were able to have breakfast together at that time. The completion of their breakfast is not about the future, but about a possibility in the past, which is already realized.