Can someone please help me with this?
Demand for the latest best selling book is given by q= -p^2 + 33p + 9 (18< or equal to p < or equal to 28) copies sold per week when the price is p dollars. Can you help me determine what price to charge to obtain the largest revenue? It costs C= 9q+100 dollars to sell q copies of this book in a week. What price should the company charge to get the largest weekly profit? What is the maximum weekly profit and how can you be sure that the profit is maximized?
Must use calculus.
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.