I'm doing a review for my final exam and this is one of the practice problems. Anyone think they could give me a hand?
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. The camper started at (6,5) on the Cartesian plane, and the ampfire 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 alon g the line x= -1. What does that make the constraint function g(x,y). Use Lagrange mulitpliers to find (x,y).
Any bit of help is greatly appreciated!