1. Find the location for a facility which minimizes the total distance traveled by all residents. 2. Find the location for a facility that minimizes the distance to the farthest city. 3. Find the location for a facility which maximizes the distance to the closest city, but the farthest city is not more than 30 miles away. (Note that the third question is not convex and thus you may get different solutions, all of them acceptable.)

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answer: it depends on what the tax percentage

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen