Minimal Cost of Fencing for a Field

A farmer wants to fence in 60,000 square feet of land in a rectangular plot along a straight highway.   The fence he plans to use along the highway costs $2 per foot, while the fence for the other three sides costs $1 per foot.  How much of each type of fence will he have to buy in order to keep expenses to a minimum?  What is the minimum expense?

Use the AM-GM Inequality to find a solution.  No calculus needed.   Once you have completed this you might find it useful to solve the problem with calculus and see some of the corresponding ideas.

Solution (do not look until after you have done your own)

Another Solution  (again, do not look until after you have done your own).   This one is not really different except for the orientation of the sketch.

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