Question: A camper has to bring a bucket of water to a campfire to put it out. He has the bucket, and must walk to the stream, fill the bucket, and then walk to the campfire. He wishes to walk the path of minimum distance. For this problem, the camper starts at (6,4) in the Cartesian plane, and the campfire is at (3,-2).

A. If (x, y) is the point in the Cartesian plane where the camper fills his bucket, find the objective function f(x, y) representing the total distance traveled.

B. Suppose the stream runs along the line x = -1. What does that make the constraint function g(x, y)? Use Lagrange multipliers to find (x, y).

C. Rework Problem 2 with the stream running along the curve \[y={{x}^{2}}\].