Suppose there are 1,000 people on a beach. The beach is 1,000 feet long and runs north to south. The people are evently distributed along the beach--that is, as one moves along the beach, there is one person every foot. For the purposes of this question, a "location" on the beach equals the number of feet from the southern end of the beach. For example, location 200 is 200 feet from the southern end of the beach, and 800 from the northern end.
There are two ice cream stands on the beach; call them A and B. Assume that everyone on the beach buys one cup of ice cream during the day and chooses the ice cream stand that is closest to them.
Initially, stand A is at location 800 and stand B is at location 200.
The "Dividing Line" is the location where people are indifferent between going to A and B. That is, everyone who is located north of the line goes to stand A, and everyone south of the line goes to B.
If the ice cream stands were each located at the middle of the beach (location 500), the longest anyone would have to walk for a cup of ice cream would be _______ feet. If the ice cream stands were located at the initial locations of 200 and 800, the longest anyone would have to walk for a cup of ice cream would be __________ feet. (Put your answers as integers with no commas).
Now suppose that each firm gets $3 of profit for each ice cream cone they sell and that stand A moves to location 600 while stand B remains at 200. Stand A will earn a profit of _______ dollars while stand B will earn a profit of ________ dollars. (Put your answers as integers with no dollar signs or commas).
Then if both stands move to the center (location 500), stand A will earn a profit of ________ dollars and stand B will earn ___________ dollars. (Put your answers as integers with no dollar signs or commas).