Question

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..

Answer 1

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