Exam 2: Differentiation: Basic Concepts

Suppose the output at a certain factory is $Q = 4 x ^ { 2 } + 3 x ^ { 3 } y ^ { 3 } + y ^ { 5 }$ units, where x is the number of hours of skilled labor used and y is the number of hours of unskilled labor. The current labor force consists of 30 hours of skilled labor and 10 hours of unskilled labor. Use calculus to estimate the change in unskilled labor y that should be made to offset a 1-hour increase in skilled labor x so that output will be maintained at its current level. Round you answer to two decimal places, if necessary.

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