Your company manufactures automobile alternators and production is partly automated through the use of robots. To meet production deadlines your company calculates that the number of laborers and robots must satisfy the constraint  xy=20000 where X is the number of laborers and y is the number of robots. Your company currently uses 200 robots and is increasing robot deployment at a rate of 18 per month. How fast is it laying off laborers?

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Q: Find the minimum value of the function f (x, y) = 16x² +81y² subject to the constraint xy = 1.

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