A 75-year-old female suffers a stroke and now has difficulty writing and production of language. this condition is most likely caused by occlusion of the:

When the left middle cerebral artery is occluded, it leads to the lack of ability to find words and difficulty in writing. Therefore in the case of the 75-year-old female stated in the question, the condition is most likely caused by occlusion of the middle cerebral artery.