A bookstore can obtain a certain book from the publisher at a cost of $3 per book. The bookstore has been offering the book at a price of $15 per copy and, at this price, has been selling 200 copies a month. The store is planning on lowering the price to stimulate sales and estimates that for each $1 reduction in the price, 20 more books will be sold each month. At what price should the bookstore sell the book to generate the greatest possible profit?

Bare with me

the profit is the # of books sold times profit per book

the number of books sold is (200 + 20)(number of $1 decreases)

200 + 20(x+15)

20[10-(x+15)]

20[-x-5]

Profit per book is (x-3)

P'(x) = 20[(-x-5)(x-3)]

P'(x) = 20(-x-5)(1) + (x-3)(-1)

P'(x) = 20(-x-5-x+3)

P'(x) = 20(-2x-2)

Setting this equal to 0 gives you x = -1

Subtracting $1 from the current price of $15 gives $14

P(14) = 20(-14-5)(14-3)

P(14) = 20(-19)(11)

P(14) = -4180

That can't be correct, its negative.