The demand for Professor Bongmore's new book is given by the function Q = 8,000 - 100p.If the cost of having the book edited and typeset is $7,000, 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
A)having it edited and typeset and selling 4,000 copies.
B)not having it edited and typeset and not selling any copies.
C)having it edited and typeset and selling 3,800 copies.
D)having it edited and typeset and selling 7,600 copies.
E)having it typeset and selling 1,900 copies.

Question

Quizplus · Accepted Answer

To maximize profits, Professor Bongmore should produce where marginal revenue (MR) equals marginal cost (MC). The marginal revenue is found by taking the derivative of the demand function with respect to quantity, giving MR = 8000 - 100Q. The marginal cost is given as $4. Setting MR equal to MC and solving for Q yields:

8000 - 100Q = 4 
Q = 3,800

So, the best choice is to have the book edited and typeset and sell 3,800 copies. This will generate a revenue of:

Q x p = 3,800 x $100 = $380,000

The total cost of producing the book is:

$7,000 + $4 x 3,800 = $23,200

Thus, the profit will be:

$380,000 - $23,200 = $356,800

Any other choice will result in lower profit or even losses.

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