At the beginning of each semester, university bookstores around the country face high demand for course

textbooks during the short period of time consisting of the first few days of the semester. Hundreds of

textbook titles are sold. Consider one textbook title sold by a given bookstore. The bookstore needs to

determine the selling price of a new copy and the selling price of a used copy.

We consider the joint pricing problem of the new and used formats of a given textbook. To simplify, we

assume that demand is deterministic; that is$,$ once we set prices we know exactly what demand would be

for each format of the textbook. Ignore integrality constraints in this problem.

The Multinomial Logit $($MNL$)$ demand model is a renowned and widely used tool in both marketing and

operations research, primarily for its effectiveness in analyzing consumer choice data. Currently, MNL

demand models remain essential for companies, serving as a fundamental instrument in comprehending

and forecasting product demand.

Let us assume that the demand for the new and used copies of the textbook under consideration follows

this model. In particular, the demands for the new and used copies of the textbook are given by the

following expressions:

dnew