1. The problem states the production function for Diana Corp as $$Q = K^{0.8} L^{0.2}$$ where $Q$ is output, $K$ is capital input, and $L$ is labor input. 2. This function shows how output $Q$ depends on inputs $K$ and $L$ with exponents indicating the output elasticity with respect to each input. 3. To analyze or use this function, you can substitute values for $K$ and $L$ to find $Q$, or explore properties like returns to scale by summing the exponents: $$0.8 + 0.2 = 1.0$$ which indicates constant returns to scale. 4. For example, if $K=10$ and $L=5$, then $$Q = 10^{0.8} \times 5^{0.2}$$ 5. Calculate each term: $$10^{0.8} = e^{0.8 \ln 10} \approx e^{1.842} \approx 6.31$$ $$5^{0.2} = e^{0.2 \ln 5} \approx e^{0.322} \approx 1.38$$ 6. Multiply these to get output: $$Q \approx 6.31 \times 1.38 = 8.71$$ 7. Thus, with $K=10$ and $L=5$, the production output $Q$ is approximately 8.71. This completes the explanation and example evaluation of the production function.