Chapter 3.2, Problem 99E

(a)

To determine

The expression of $R\left(x\right)$ by when the demand for a new computer game can be modeled by $p\left(x\right)=53.5-8\ln x$. Here, $p\left(x\right)$ is the price that consumer pay in dollar and $x$ is the number of games sold in thousand. The expression of total revenue is calculated by $R\left(x\right)=xp\left(x\right)$.

(b)

To determine

To calculate: The marginal revenue, $R^{\prime }\left(x\right)$ of the function $R\left(x\right)=xp\left(x\right)$. When the demand for a new computer game can be modeled by $p\left(x\right)=53.5-8\ln x$.

(c)

To determine

To calculate: The price at which revenue will be maximum of the function $p\left(x\right)$, when the demand for a new computer game can be modeled by $p\left(x\right)=53.5-8\ln x$. The expression of total revenue is calculated by $R\left(x\right)=xp\left(x\right)$.