While the quantity of a product demanded by consumers is often a function of the price of the product, the demand for a product may also depend on the price of other products. For instance, the demand for blue jeans at a clothing store may be affected not only by the price of the jeans themselves, but also by the price of khakis.
Suppose we have two goods whose respective prices are \(p_1\) and \(p_2\text{.}\) The demand for these goods, \(q_1\) and \(q_2\text{,}\) depend on the prices as
The seller would like to set the prices \(p_1\) and \(p_2\) in order to maximize revenue. We will assume that the seller meets the full demand for each product. Thus, if we let \(R\) be the revenue obtained by selling \(q_1\) items of the first good at price \(p_1\) per item and \(q_2\) items of the second good at price \(p_2\) per item, we have
\begin{equation*}
R = p_1q_1 + p_2q_2.
\end{equation*}
