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A rectangular field is to be enclosed with a fence. One side of the fence is against an existing fence, so that no fence is needed on that side.

A rectangular field is to be enclosed with a fence. One side of the fence is against an existing fence, so that no fence is needed on that side. If material for the fence costs $2 per foot for the two ends and $4 per foot for the side parallel to the existing fence, find the dimensions of the field of largest area that can be enclosed for $1,000.

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