A paper mill produces two types of paper: paper for books and paper for magazines. The profit contributions are $214 for each ton of paper for books and $261 for each ton of paper for magazines. Each ton of paper for books requires two tons of spruce and four tons of fir; each ton of paper for magazines requires two tons of spruce and two tons of fir. The company must supply at least 25,000 tons of paper for books and at least 20,000 tons of paper for magazines a year. The yearly availability of materials is 278,000 tons of spruce and 420,000 tons of fir. The chief executive officer imposes an additional restriction that the amount of paper manufactured for magazines should be no more than a half of the amount of paper manufactured for books. Determine the amount of paper (in tons) for magazines and the amount of paper (in tons) books to maximize the total profit.
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