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In a proportional cake-cutting, each person receives a piece that he values as at least 1/n of the value of the entire cake. In the example cake, a proportional division can be achieved by giving all the vanilla and 4/9 of the chocolate to George (for a value of 6.66), and the other 5/9 of the chocolate to Alice (for a value of 5). In symbols:
Packaged chocolate in the Ghirardelli Chocolate Company. Chocolate, prevalent throughout the world, is a steadily growing, US$50 billion-a-year worldwide business as of 2009. [139] As of 2006, Europe accounted for 45% of the world's chocolate revenue, [140] and the US spent $20 billion in 2013. [141]
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