Scenario

Two vendors, Ms. Bud and Ms. Weiser, operate on a beach. They are required to charge the same price, but they can choose where to locate themselves on the beach. Their customers, sunbathers, do not like to be near each other, so they are spread evenly along the beach. Sunbathers are also averse to walking, so they purchase one can of beer from the vendor closest to them.

Where on the beach will the vendors, seeking large sales, locate themselves?

Hint: If one vendor, say, Ms. Bud, had already chosen her location, where should her rival, Ms. Weiser, place herself? 

Analyze the given situation (the scenario) from both vendor's perspective, and present either one solution or compare several possible solutions.