The demand for Professor Bongmore's new book is given by the function Q = 5,000 - 100p. If the cost of having the book typeset is $9,000, if the marginal cost of printing an extra copy is $4, and if he has no other costs, then he would maximize his profits by

Question

Quizplus · Accepted Answer

Profits are maximized when marginal revenue equals marginal cost. Marginal revenue is the derivative of the demand function, which in this case is MR = 5000 - 200p.
We can find the optimal price by setting MR = MC:
5000 - 200p = 4
p = 24.80
Now that we have the optimal price, we can find the optimal quantity by plugging it back into the demand function:
Q = 5000 - 100(24.80)
Q = 2300
Therefore, the best choice is to have it typeset and sell 2,300 copies.

The Demand for Professor Bongmore's New Book Is Given by the Function