\text{Average Cost}(50) = \frac{0.02(50)^2 + 72}{50} = \frac{0.02 \cdot 2500 + 72}{50} = \frac{50 + 72}{50} = 2.44 [Step-by-Step] \text{Average Cost}(50) = \frac{0.02(50)^2 + 72}{50} = \frac{0.02 \cdot 2500 + 72}{50} = \frac{50 + 72}{50} = 2.44
C. Set the marginal cost function necessarily [Solution] \text{Marginal Cost}(x) = \frac{dK(x)}{dx} = \frac{d}{dx}(0.02x^2 + 72) = 0.04x [Step-by-Step] \text{Marginal Cost}(x) = \frac{dK(x)}{dx} = \frac{d}{dx}(0.02x^2 + 72) = 0.04x
D. Calculate the marginal costs for 50 products necessarily [Solution] \text{Marginal Cost}(50) = 0.04 \cdot 50 = 2 [Step-by-Step] \text{Marginal Cost}(50) = 0.04 \cdot 50 = 2
E. At what quantity does one reach the operating optimum necessarily [Solution] \text{Operating Optimum is reached when Marginal Cost equals Average Cost} \text{Set } 0.04x = \frac{0.02x^2 + 72}{x} 0.04x = 0.02x + \frac{72}{x} 0.02x^2 = 72 x^2 = 3600 x = 60 [Step-by-Step] \text{Operating Optimum is reached when Marginal Cost equals Average Cost} \text{Set } 0.04x = \frac{0.02x^2 + 72}{x} 0.04x = 0.02x + \frac{72}{x} 0.02x^2 = 72 x^2 = 3600 x = 60