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Suppose that there are two ice cream vendors on a beach which is represented by the 0-1 interval

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Suppose that there are two ice cream vendors on a beach which is represented by the 0-1 interval. Customers are uniformly distributed along that interval. The vendors simultaneously select a position. Cus- tomers go to the closest vendor and split themselves evenly if the ven- dors choose an identical position. Each vendors want to maximize its number of customers. Which location should the vendors choose in the 0-1 interval, why?