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Two ice-cream stands are deciding where to set up along a 1-mile beach. The people are uniformly located along the beach, and each person sitting on the beach buys exactly 1 ice-cream cone per day from the nearest stand. Each ice-cream seller wants the maximum number of customers. Where along the beach will the two stands locate? Of which result in this chapter does this outcome remind you?
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here, we're working with what is known as the median voter theorem. And we're going to be able to answer this question here under this understanding of the medium voter theorem. So we're looking at an example in which we have an 11 mile beach which has people uniformly located along it. And there are two ice cream sellers on this beach, each of whom wants to maximize their profits. So working under this assumption that each person or customer is going to choose the ice cream stand, which is closest to them. Where should these sellers locate their stands in order to maximize their profits? Well, considering the median voter theorem, this idea that people are going to choose that option, which is closest to what they want, we could expect that each of these sellers is likely to place their stands right in the in the middle of the beach, Right? And if we wanted to draw a little picture to give ourselves a better idea, suppose here is our 11 mile beach and somewhere along it, right? We have all of our customers supposing, you know, people are all equally dispersed. We were told, well, if these sellers want to maximize their profits, what they're going to do is place there stands right in here, right? We're gonna have to sellers right in the middle because what this allows them to do is get each one of the sellers on either side of them versus if one of the sellers had instead placed there, stand all the way over here, they would be likely to get maybe just a couple, maybe just these two. Whereas all of the other ones, maybe they could get this one as well, so they get three. But the other seller sitting in here would then get five sellers as compared to the one over here would only have three so you can see that. But placing their stand in the middle of the beach in the median, if we want to call it that, then they are going to get the greatest amount of customers, meaning they'll be able to maximize their profits. So this is telling us that these sellers should place their stands right in the middle of this beach.
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