1. The problem is to find the correct premium subscription price using the revenue function, which is linear. 2. The revenue function is given by $$R(p) = p \times q(p)$$ where $p$ is the price and $q(p)$ is the quantity sold at price $p$. 3. Since the revenue function is linear, $q(p)$ can be expressed as a linear function of $p$, for example, $q(p) = a - bp$ where $a$ and $b$ are constants. 4. Therefore, the revenue function becomes $$R(p) = p(a - bp) = ap - bp^2$$. 5. To find the price $p$ that maximizes revenue, take the derivative of $R(p)$ with respect to $p$ and set it to zero: $$\frac{dR}{dp} = a - 2bp = 0$$ 6. Solve for $p$: $$a - 2bp = 0 \Rightarrow 2bp = a \Rightarrow p = \frac{a}{2b}$$ 7. This $p$ is the premium subscription price that maximizes revenue. 8. Without specific values for $a$ and $b$, this is the general formula to find the correct premium subscription price.