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**HallsofIvy** You got upset because no one had responded within 2 hours? We do have lives, you know!

Revenue is, of course, price per book times number of books. Here that is pq= p(-p^2+ 33p+ 9)= -p^3+ 33p+ 9. Set the derivative of that equal to 0 and solve for p.

Profit is revenue minus costs: Profit= -p^3+ 33p+ 9- (9q+100)= -p^3+ 33p+ 9- 9(-p^2+ 33p+ 9)- 100= -p^3+ 9p^2- 265p- 172. Again, set the derivative of that equal to 0 and solve for p. To see if that really maximizes the profit, see what happens if you change the price by, say, 1 penny.