June 30, 2015

Homework Help: Calc

Posted by Ben on Sunday, November 25, 2007 at 1:46pm.

Demand is q=-p^2+33p+9 copies of a book sold per week when price is p dollars. Can you help determine what price the company should charge to get the largest revenue?
I solved this as a Max Revenue problem and got x=0 and x=22 so the books should be sold for $22 each. IS THIS RIGHT?

Also, cost is C=9q+100 dollars to sell q copies of a book in a week. What price should the company charge to get the largest weekly profit? What is the max possible profit weekly profit and how can you be certain that the profit is maximized?
I got the profit function to be P=p(-p^2+33p+9)-9(-p^2+33p+9)+100. I simplified this to P=(-p^2+33+9)(p-9+100). I then took the derivative using the product rule to get P'=-2p+33(p-9+100)+(1)(-p^2+33p+9). I know I then need to set this equal to zero if it is right, I then have to factor and say which value maximizes profit. IS THIS RIGHT? Please help me to solve this part, I do not know how to solve P' equal to zero and factor

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