?A manufacturer has modeled its yearly production function (the value of its entire

Chapter 12, Problem 46

(choose chapter or problem)

A manufacturer has modeled its yearly production function  (the value of its entire production, in millions of dollars) as a Cobb-Douglas function

where  is the number of labor hours (in thousands) and  is the invested capital (in millions of dollars). Suppose that when  and , the labor force is decreasing at a rate of 2000 labor hours per year and capital is increasing at a rate of  per year. Find the rate of change of production.

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