Assume that if the price of a certain book is p dollars, then it will sell x copies where. x = 7000 (1 - p/35). Suppose the dollar cost of producing those x copies is 15000 + 2.5x ... Finally, assume that the company will not sell this book for more than $35. Determine the. price for the book that will maximize profit ...

Profit = Income - Cost

I = p * x; C = 15,000 - 2.5 x

P = 7000 p (1 - p/35) - 15,000 - 2.5 (7000 (1 - p/35) =

=7,000 p - 200 p² - 15,000 - 17,500 + 500 p = - 200 p² + 7,500 p - 32,500

P ' = - 400 p + 7,500

- 400 p + 7,500 = 0

400 p = 7,500

p = 7,500 : 400 = $18.75

P'' = - 400 < 0 (this is a maximum)

Answer: The price for the book that will maximize the profit is $18.75