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A textbook publisher puts out 72 new books each year, which are classified as elementary intermediate and advanced. The company's policy for new books is to publish at least four advanced books, at least 3 times as many elementary books as intermediate books, and at least twice as many intermediate books as advanced books. On the average, the annual profits are $8000 for each elementary book, $7000 for each intermediate book, and $1000 for each advanced book. How many new books of each type should be published to maximize the annual profit while conforming to company policy?

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