Fresh day Senior, let's solve. Step 1: Determine the revenue function. The demand function is given by $p = 40q$. Revenue $R$ is calculated as the product of price $p$ and quantity $q$: $$R = p \times q$$ Substitute the given demand function into the revenue formula: $$R = (40q) \times q$$ $$R = 40q^2$$ Note: A typical demand function shows that price decreases as quantity increases. The given function $p=40q$ implies that price increases with quantity, which is unusual for a demand function. Step 2: Analyze the revenue function for maximization. The revenue function is $R(q) = 40q^2$. This is a quadratic function representing a parabola that opens upwards. For production levels $q \ge 0$, the value of $R(q)$ continuously increases as $q$ increases. To find a maximum, we would typically take the derivative and set it to zero: $$\frac{dR}{dq} = \frac{d}{dq}(40q^2) = 80q$$ Setting $\frac{dR}{dq} = 0$ gives $80q = 0$, which means $q = 0$. This corresponds to the minimum revenue ($R=0$), not a maximum. Since the function $R(q) = 40q^2$ increases indefinitely for $q > 0$, there is no finite maximum revenue. 1) At what level of production is revenue maximized? Based on the given demand function $p=40q$, the revenue function $R(q) = 40q^2$ continuously increases as the level of production $q$ increases (for $q \ge 0$). Therefore, there is no finite level of production at which revenue is maximized. Revenue can be made arbitrarily large by increasing production. $$\boxed{\text{No finite level of production}}$$ 2) What is the maximum revenue at this point? Since there is no finite level of production that maximizes revenue, there is no finite maximum revenue. $$\boxed{\text{No finite maximum revenue}}$$ Send me the next one 📸