A rancher plans to use an existing stone wall and the side of a barn as a boundary for two adjacent rectangular corrals.Fencing for the perimeter costs 10 per foot.To separate the corrals,a fence that costs 8 per foot will divide the region.The total area of the two corrals is to be 7,000 square feet.Use Lagrange multipliers to find the dimensions that will minimize the cost of the fencing. 
Definitions:
Intensity
The degree of strength, force, or energy of a stimulus or behavior.
Amplitude
The height or strength of a wave signal, which in the context of sound refers to its loudness and in light, its brightness.
Sound Wave
A wave of compression and rarefaction, by which sound is propagated in an elastic medium such as air.
Loudness
The dimension of auditory experience related to the intensity of a pressure wave.
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