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Use the method of Lagrange multipliers to solve this exercise. I want to fence in a...

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 $6 per foot, and the fencing for the north and south sides costs only $3 per foot. I have a budget of $120 for the project. What is the largest area I can enclose?

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Answer #1

cost of the fencing

C=6(2x)+3(2y)

C=12x+6y ----------(1)

120=12x+6y

2x+y=20 -------(2)

Area of rectangular patch

A=xy ----------(3)

Langrange multipliers

From equation (2)

Maximum area

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