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Use the method of Lagrange multipliers to solve this exercise. I want to fence in a rectangular vegetable patch. The fencing for the east and

Use the method of Lagrange multipliers to solve this exercise.

I want to fence in a rectangular vegetable patch. The fencing for the east and west sides costs $4per foot, and the fencing for the north and south sides costs only $2per foot. I have a budget of $64for the project. What is the largest area I can enclose?

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