economicsAt a certain factory, output is given by $Q=60 K^{1 / 3} L^{2 / 3}$ units, where $K$ is the capital investment (in thousands of dollars) and $L$ is the size of the labor force, measured in workerhours. If output is kept constant, at what rate is capital investment changing at a time when $K=8$, $L=1,000$, and $L$ is increasing at the rate of 25 worker-hours per week?
[Note: Output functions of the general form $Q=A K^\alpha L^{1-\alpha}$, where $A$ and $\alpha$ are constants with $0 \leq \alpha \leq 1$, are called Cobb-Douglas production functions. Such functions appear in examples and exercises throughout this text, especially in
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