For the sentence in question, 'interested in' is the word that is most nearly opposite to 'indifferent' and correctly fills the gap, indicating that management is expected to show active concern for the workers' welfare.
To find the word that is most nearly opposite in meaning to indifferent and that fits correctly in the gap, we need to understand that 'indifferent' means having a lack of interest or concern. Therefore, the opposite would be a word that suggests active concern or attention. Among the provided options, the word that is opposite in meaning to 'indifferent' and that fills the gap appropriately in the sentence 'The workers expected management to be…rather than indifferent to their welfare.' is 'interested in'. This is because if management is 'interested in' the workers' welfare, it implies that they have an active concern for their well-being which is the opposite of being indifferent.